5.6 & 5.7 BONUS practice: due 2/27/24
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Last updated over 1 year ago
32 questions
Note from the author:
For bonus points on the exam you must also turn in the recording document.
For bonus points on the exam you must also turn in the recording document.
Required
1
The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution. Give the Normal Model for this situation using the correct notation: N(#, #)
The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution. Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution. What proportion of children have a cholesterol level above 200 mg/dl'?
1. Calculate the z-score.2. Use the z-table to find the decimal proportion ABOVE the z-score (find the z score, subtract the proportion from 1)3. Round the decimal proportion to three or four places past the decimal.
The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution. What proportion of children have a cholesterol level above 200 mg/dl'?
1. Calculate the z-score.
2. Use the z-table to find the decimal proportion ABOVE the z-score (find the z score, subtract the proportion from 1)
3. Round the decimal proportion to three or four places past the decimal.
Required
1
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. In healthy Alaskan brown bears, the amount of porphyrin in the bloodstream (in mg/dl) has approximate normal distribution with a mean of 38 mg/dl and a standard deviation of 12.
Give the Normal Model for this situation using the correct notation: N(#, #)
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. In healthy Alaskan brown bears, the amount of porphyrin in the bloodstream (in mg/dl) has approximate normal distribution with a mean of 38 mg/dl and a standard deviation of 12.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. In healthy Alaskan brown bears, the amount of porphyrin in the bloodstream (in mg/dl) has approximate normal distribution with a mean of 38 mg/dl and a standard deviation of 12. What proportion of these bears have between 27.5 and 67.5 mg/dl porphyrin in their bloodstream?
1. Calculate the z-scores.2. Use the z-table to find the proportion to the left for both z-scores, find the difference between the two.3. Round the decimal proportion between to three or four places past the decimal.
Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. In healthy Alaskan brown bears, the amount of porphyrin in the bloodstream (in mg/dl) has approximate normal distribution with a mean of 38 mg/dl and a standard deviation of 12.
What proportion of these bears have between 27.5 and 67.5 mg/dl porphyrin in their bloodstream?
1. Calculate the z-scores.
2. Use the z-table to find the proportion to the left for both z-scores, find the difference between the two.
3. Round the decimal proportion between to three or four places past the decimal.
Required
1
A forest products company claims that the amount of usable lumber in its harvested trees averages 172 cubic feet and has standard deviation of 12.4 cubic feet. Assume that these amounts have approximately a normal distribution.
Give the Normal Model for this situation using the correct notation: N(#, #)
A forest products company claims that the amount of usable lumber in its harvested trees averages 172 cubic feet and has standard deviation of 12.4 cubic feet. Assume that these amounts have approximately a normal distribution.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
A forest products company claims that the amount of usable lumber in its harvested trees averages 172 cubic feet and has standard deviation of 12.4 cubic feet. Assume that these amounts have approximately a normal distribution. What proportion of trees contains more than 150 cubic feet?
1. Calculate the z-score.2. Use the z-table to find the proportion to the right of the z-score. (find the z score, subtract the proportion from 1)3. Round the decimal proportion to the right of the z-score to three places past the decimal.
A forest products company claims that the amount of usable lumber in its harvested trees averages 172 cubic feet and has standard deviation of 12.4 cubic feet. Assume that these amounts have approximately a normal distribution.
What proportion of trees contains more than 150 cubic feet?
1. Calculate the z-score.
2. Use the z-table to find the proportion to the right of the z-score. (find the z score, subtract the proportion from 1)
3. Round the decimal proportion to the right of the z-score to three places past the decimal.
Required
1
GPAs of freshman biology majors at a certain university have approximately the normal distribution with the mean 2.87 and the standard deviation is 0.34.
Give the Normal Model for this situation using the correct notation: N(#, #)
GPAs of freshman biology majors at a certain university have approximately the normal distribution with the mean 2.87 and the standard deviation is 0.34.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
GPAs of freshman biology majors at a certain university have approximately the normal distribution with the mean 2.87 and the standard deviation is 0.34. What proportion of freshman biology majors have GPA above 3.50?
1. Calculate the z-score.2. Use the z-table to find the proportion to the right of the z-score.3. If the question asks for 'above' or 'at least' or 'top' then subtract the proportion from 1.04. Round the decimal proportion to the right of the z-score to three places past the decimal.
GPAs of freshman biology majors at a certain university have approximately the normal distribution with the mean 2.87 and the standard deviation is 0.34.
What proportion of freshman biology majors have GPA above 3.50?
1. Calculate the z-score.
2. Use the z-table to find the proportion to the right of the z-score.
3. If the question asks for 'above' or 'at least' or 'top' then subtract the proportion from 1.0
4. Round the decimal proportion to the right of the z-score to three places past the decimal.
Required
1
Mensa is an organization whose members possess IQs in the top 2% of the population. The IQs are normally distributed with a mean of 100 and a standard deviation of 15.
Give the Normal Model for this situation using the correct notation: N(#, #)
Mensa is an organization whose members possess IQs in the top 2% of the population.
The IQs are normally distributed with a mean of 100 and a standard deviation of 15.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
Mensa is an organization whose members possess IQs in the top 2% of the population. If the IQs are normally distributed with a mean of 100 and a standard deviation of 15, what is the minimum IQ necessary for admission?
1. Find the proportion to the left.2. Find the z score closest to the proportion to the left.2. Use the z-table to find the z-score.3. Set up the z score formula and solve for the value (x)4. Round the decimal to one place past the decimal point.
Mensa is an organization whose members possess IQs in the top 2% of the population.
If the IQs are normally distributed with a mean of 100 and a standard deviation of 15, what is the minimum IQ necessary for admission?
1. Find the proportion to the left.
2. Find the z score closest to the proportion to the left.
2. Use the z-table to find the z-score.
3. Set up the z score formula and solve for the value (x)
4. Round the decimal to one place past the decimal point.
Required
1
Healthy 10-week-old domestic kittens have average weight 24.5 oz. with a standard deviation of 5.25 oz. The distribution is approximately normal. A kitten is designated as dangerously underweight when, at 10 weeks, it weighs less than 10.0 oz.
Give the Normal Model for this situation using the correct notation: N(#, #)
Healthy 10-week-old domestic kittens have average weight 24.5 oz. with a standard deviation of 5.25 oz. The distribution is approximately normal. A kitten is designated as dangerously underweight when, at 10 weeks, it weighs less than 10.0 oz.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
Healthy 10-week-old domestic kittens have average weight 24.5 oz. with a standard deviation of 5.25 oz. The distribution is approximately normal. A kitten is designated as dangerously underweight when, at 10 weeks, it weighs less than 10.0 oz. What proportion of healthy kittens will designated as dangerously underweight?
1. Calculate the z-score.2. Use the z-table to find the decimal proportion below the z-score3. Round the decimal proportion to three places past the decimal.
Healthy 10-week-old domestic kittens have average weight 24.5 oz. with a standard deviation of 5.25 oz. The distribution is approximately normal. A kitten is designated as dangerously underweight when, at 10 weeks, it weighs less than 10.0 oz.
What proportion of healthy kittens will designated as dangerously underweight?
1. Calculate the z-score.
2. Use the z-table to find the decimal proportion below the z-score
3. Round the decimal proportion to three places past the decimal.
Required
1
The length of the elephant pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 525 days and standard deviation 32 days.
Give the Normal Model for this situation using the correct notation: N(#, #)
The length of the elephant pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 525 days and standard deviation 32 days.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
The length of the elephant pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 525 days and standard deviation 32 days. What proportion of pregnancies last between 510 and 540 days (that’s between 17 and 18 months)?
1. Calculate both z-scores.2. Use the z-table to find the proportion to the left for both z-scores3. Find the proportion between the two points by subtracting, find the difference between the two.4. Round the decimal proportion between the z-scores to three places past the decimal.
The length of the elephant pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 525 days and standard deviation 32 days.
What proportion of pregnancies last between 510 and 540 days (that’s between 17 and 18 months)?
1. Calculate both z-scores.
2. Use the z-table to find the proportion to the left for both z-scores
3. Find the proportion between the two points by subtracting, find the difference between the two.
4. Round the decimal proportion between the z-scores to three places past the decimal.
Required
1
At two years of age, sardines inhabiting Japanese waters have a length distribution that is approximately normal with mean 20.20 cm and standard deviation 0.65 cm.
Give the Normal Model for this situation using the correct notation: N(#, #)
At two years of age, sardines inhabiting Japanese waters have a length distribution that is approximately normal with mean 20.20 cm and standard deviation 0.65 cm.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
At two years of age, sardines inhabiting Japanese waters have a length distribution that is approximately normal with mean 20.20 cm and standard deviation 0.65 cm. What proportions of these sardines are between 19.0 and 21.0 cm long?
1. Calculate both z-scores.2. Use the z-table to find the proportion to the left for both z-scores3. Find the area between the two points by subtracting, find the difference between the two.4. Round the decimal proportion between the z-scores to three places past the decimal.
At two years of age, sardines inhabiting Japanese waters have a length distribution that is approximately normal with mean 20.20 cm and standard deviation 0.65 cm.
What proportions of these sardines are between 19.0 and 21.0 cm long?
1. Calculate both z-scores.
2. Use the z-table to find the proportion to the left for both z-scores
3. Find the area between the two points by subtracting, find the difference between the two.
4. Round the decimal proportion between the z-scores to three places past the decimal.
Required
1
A manufacturer contracts to supply ball bearings with diameters between 24.60 millimeters and 25.40 millimeters. Product analysis indicates that the ball bearings manufactured have diameters that are normally distributed with a mean of 25.10 millimeters and a standard deviation of 0.20 millimeters.
Give the Normal Model for this situation using the correct notation: N(#, #)
A manufacturer contracts to supply ball bearings with diameters between 24.60 millimeters and 25.40 millimeters. Product analysis indicates that the ball bearings manufactured have diameters that are normally distributed with a mean of 25.10 millimeters and a standard deviation of 0.20 millimeters.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
A manufacturer contracts to supply ball bearings with diameters between 24.60 millimeters and 25.40 millimeters. Product analysis indicates that the ball bearings manufactured have diameters that are normally distributed with a mean of 25.10 millimeters and a standard deviation of 0.20 millimeters. What percentage of ball bearings fail to satisfy the contract specifications? (they are above or below the specifications)
1. Calculate the two z-scores.2. Use the z-table to find the proportion to the left for the low z-score.3. Use the z-table to find the proportion to the right for the high z-score. (you will need to subtract from 1.0) 4. Add the two proportions to find the total.5. Round the decimal proportion above and below the z-scores to three places past the decimal.
A manufacturer contracts to supply ball bearings with diameters between 24.60 millimeters and 25.40 millimeters. Product analysis indicates that the ball bearings manufactured have diameters that are normally distributed with a mean of 25.10 millimeters and a standard deviation of 0.20 millimeters.
What percentage of ball bearings fail to satisfy the contract specifications? (they are above or below the specifications)
1. Calculate the two z-scores.
2. Use the z-table to find the proportion to the left for the low z-score.
3. Use the z-table to find the proportion to the right for the high z-score. (you will need to subtract from 1.0)
4. Add the two proportions to find the total.
5. Round the decimal proportion above and below the z-scores to three places past the decimal.
Required
1
GPAs of freshman biology majors at a certain university have approximately the normal distribution with the mean 2.87 and the standard deviation is 0.34. Students are thrown out of school if their GPA falls below 2.00.
Give the Normal Model for this situation using the correct notation: N(#, #)
GPAs of freshman biology majors at a certain university have approximately the normal distribution with the mean 2.87 and the standard deviation is 0.34. Students are thrown out of school if their GPA falls below 2.00.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
GPAs of freshman biology majors at a certain university have approximately the normal distribution with the mean 2.87 and the standard deviation is 0.34. Students are thrown out of school if their GPA falls below 2.00. What proportion of all freshman biology majors are thrown out?
1. Calculate the z-score.2. Use the z-table to find the decimal proportion below the z-score3. Round the decimal proportion to three places past the decimal.
GPAs of freshman biology majors at a certain university have approximately the normal distribution with the mean 2.87 and the standard deviation is 0.34. Students are thrown out of school if their GPA falls below 2.00.
What proportion of all freshman biology majors are thrown out?
1. Calculate the z-score.
2. Use the z-table to find the decimal proportion below the z-score
3. Round the decimal proportion to three places past the decimal.
Required
1
The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution.
Give the Normal Model for this situation using the correct notation: N(#, #)
The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution. How high are the levels for the highest 2.5% of all children?
1. Change the % to a decimal proportion.2. If the question asks for 'above' or 'at least' or 'top' then subtract from 1.03. Use the middle of the table to find the closest proportion, then look at the margins to find the corresponding z-score.4. Use the z-score formula to find the cholesterol level (set up the equation and solve for x). Round to one place past the decimal.
The mean cholesterol level in children is 175 mg/dl with standard deviation 35 mg/dl. Assume this level varies from child to child according to an approximate normal distribution. How high are the levels for the highest 2.5% of all children?
1. Change the % to a decimal proportion.
2. If the question asks for 'above' or 'at least' or 'top' then subtract from 1.0
3. Use the middle of the table to find the closest proportion, then look at the margins to find the corresponding z-score.
4. Use the z-score formula to find the cholesterol level (set up the equation and solve for x). Round to one place past the decimal.
Required
1
A manufacturer of bulbs for movie projectors advertises a life of 50 hours. A study of these bulbs indicates that their lives are normally distributed with a mean of 61 hours and a standard deviation of 6.3 hours.
Give the Normal Model for this situation using the correct notation: N(#, #)
A manufacturer of bulbs for movie projectors advertises a life of 50 hours. A study of these bulbs indicates that their lives are normally distributed with a mean of 61 hours and a standard deviation of 6.3 hours.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
A manufacturer of bulbs for movie projectors advertises a life of 50 hours. A study of these bulbs indicates that their lives are normally distributed with a mean of 61 hours and a standard deviation of 6.3 hours. What is the proportion of bulbs that fail to last as long as the manufacturer claims?
1. Calculate the z-score.2. Use the z-table to find the decimal proportion below the z-score3. Round the decimal proportion to three places past the decimal.
A manufacturer of bulbs for movie projectors advertises a life of 50 hours. A study of these bulbs indicates that their lives are normally distributed with a mean of 61 hours and a standard deviation of 6.3 hours.
What is the proportion of bulbs that fail to last as long as the manufacturer claims?
1. Calculate the z-score.
2. Use the z-table to find the decimal proportion below the z-score
3. Round the decimal proportion to three places past the decimal.
Required
1
A forest products company claims that the amount of usable lumber in its harvested trees averages 172 cubic feet and has standard deviation of 12.4 cubic feet. Assume that these amounts have approximately a normal distribution.
Give the Normal Model for this situation using the correct notation: N(#, #)
A forest products company claims that the amount of usable lumber in its harvested trees averages 172 cubic feet and has standard deviation of 12.4 cubic feet. Assume that these amounts have approximately a normal distribution.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
A forest products company claims that the amount of usable lumber in its harvested trees averages 172 cubic feet and has standard deviation of 12.4 cubic feet. Assume that these amounts have approximately a normal distribution. What proportion of trees contains between 175 and 190 cubic feet?
1. Calculate both z-scores.2. Use the z-table to find the proportion to the left for both z-scores, do not round.3. Find the area between the two points by subtracting the proportions, find the difference.4. Round the decimal proportion between the z-scores to three places past the decimal.
A forest products company claims that the amount of usable lumber in its harvested trees averages 172 cubic feet and has standard deviation of 12.4 cubic feet. Assume that these amounts have approximately a normal distribution.
What proportion of trees contains between 175 and 190 cubic feet?
1. Calculate both z-scores.
2. Use the z-table to find the proportion to the left for both z-scores, do not round.
3. Find the area between the two points by subtracting the proportions, find the difference.
4. Round the decimal proportion between the z-scores to three places past the decimal.
Required
1
In studying ocean conditions, the Bureau of Fisheries found that for one location, the August water temperatures (in degrees Fahrenheit) were normally distributed with a mean of 83.6 and a standard deviation of 2.4.
Give the Normal Model for this situation using the correct notation: N(#, #)
In studying ocean conditions, the Bureau of Fisheries found that for one location, the August water temperatures (in degrees Fahrenheit) were normally distributed with a mean of 83.6 and a standard deviation of 2.4.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
In studying ocean conditions, the Bureau of Fisheries found that for one location, the August water temperatures (in degrees Fahrenheit) were normally distributed with a mean of 83.6 and a standard deviation of 2.4. For a randomly selected time in August, find the probability that the water temperature is between 83.6 and 87.0 degrees.
1. Calculate both z-scores.2. Use the z-table to find the proportion to the left for both z-scores.3. Find the area between the two points by subtracting, do not round.4. Round the decimal proportion between the z-scores to three places past the decimal.
In studying ocean conditions, the Bureau of Fisheries found that for one location, the August water temperatures (in degrees Fahrenheit) were normally distributed with a mean of 83.6 and a standard deviation of 2.4.
For a randomly selected time in August, find the probability that the water temperature is between 83.6 and 87.0 degrees.
1. Calculate both z-scores.
2. Use the z-table to find the proportion to the left for both z-scores.
3. Find the area between the two points by subtracting, do not round.
4. Round the decimal proportion between the z-scores to three places past the decimal.
Required
1
Healthy 10-week-old domestic kittens have average weight 24.5 oz. with a standard deviation of 5.25 oz. The distribution is approximately normal. What are the first and third quartiles of the kitten weights? (25% of the kitten weighs less than Q1; 75% weigh more. 75%of the kittens weigh less that Q3; 25% weigh more)
Give the Normal Model for this situation using the correct notation: N(#, #)
Healthy 10-week-old domestic kittens have average weight 24.5 oz. with a standard deviation of 5.25 oz. The distribution is approximately normal.
What are the first and third quartiles of the kitten weights? (25% of the kitten weighs less than Q1; 75% weigh more. 75%of the kittens weigh less that Q3; 25% weigh more)
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
Healthy 10-week-old domestic kittens have average weight 24.5 oz. with a standard deviation of 5.25 oz. The distribution is approximately normal. Use the first and third quartiles of the kitten weights to calculate the IQR. (25% of the kitten weighs less than Q1; 75%of the kittens weigh less that Q3)
What is the interquartile range (IQR) for the kitten weights?
1. Change the percentiles for Q1 and Q3 to proportions.2. Use both proportions to find the closest proportions in the center of the z-table and then the corresponding z-scores.3. Change the z-scores to actual weights of the kittens, solve both z score formulas for x.4. Give the range for the middle 50% of the kitten weights as one number (Q3-Q1, use actual data values) in ounces rounded to three places past the decimal.5. Make sure you include units to give meaning!
Healthy 10-week-old domestic kittens have average weight 24.5 oz. with a standard deviation of 5.25 oz. The distribution is approximately normal.
Use the first and third quartiles of the kitten weights to calculate the IQR. (25% of the kitten weighs less than Q1; 75%of the kittens weigh less that Q3)
What is the interquartile range (IQR) for the kitten weights?
1. Change the percentiles for Q1 and Q3 to proportions.
2. Use both proportions to find the closest proportions in the center of the z-table and then the corresponding z-scores.
3. Change the z-scores to actual weights of the kittens, solve both z score formulas for x.
4. Give the range for the middle 50% of the kitten weights as one number (Q3-Q1, use actual data values) in ounces rounded to three places past the decimal.
5. Make sure you include units to give meaning!
Required
1
At two years of age, sardines inhabiting Japanese waters have a length distribution that is approximately normal with mean 20.20 cm and standard deviation 0.65 cm.
Give the Normal Model for this situation using the correct notation: N(#, #)
At two years of age, sardines inhabiting Japanese waters have a length distribution that is approximately normal with mean 20.20 cm and standard deviation 0.65 cm.
Give the Normal Model for this situation using the correct notation: N(#, #)
Required
1
At two years of age, sardines inhabiting Japanese waters have a length distribution that is approximately normal with mean 20.20 cm and standard deviation 0.65 cm. What is the length of the longest 15% of all these sardines?
1. Change the % to a decimal proportion.2. If the question asks for 'above' or 'at least' or 'top' then subtract from 1.03. Use the middle of the table to find the closest proportion, then look at the margins to find the corresponding z-score.4. Use the z-score formula to find the length of the sardines, set up the formula and solve for x. Round to three places past the decimal. Use units in your answer!
At two years of age, sardines inhabiting Japanese waters have a length distribution that is approximately normal with mean 20.20 cm and standard deviation 0.65 cm.
What is the length of the longest 15% of all these sardines?
1. Change the % to a decimal proportion.
2. If the question asks for 'above' or 'at least' or 'top' then subtract from 1.0
3. Use the middle of the table to find the closest proportion, then look at the margins to find the corresponding z-score.
4. Use the z-score formula to find the length of the sardines, set up the formula and solve for x.
Round to three places past the decimal.
Use units in your answer!