A data set has a normal distribution with a mean of 480 grams and a standard deviation of 20 grams. A value from the data set is randomly chosen. What is the probability that the value is 480 grams or less?
The probability that a randomly chosen value is 480 grams or less is _______.
(Round the probability to the nearest hundredths.)
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Question 2
2.
A data set has a normal distribution with a mean of 480 grams and a standard deviation of 20 grams. A value from the data set is randomly chosen. What is the probability that the value is between 460 grams and 500 grams?
The probability that a randomly chosen value is between 460 grams or 500 grams is _______.
(Round the probability to the nearest hundredths.)
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Question 3
3.
A data set has a normal distribution with a mean of 480 grams and a standard deviation of 20 grams. A value from the data set is randomly chosen. What is the probability that the value is between 440 grams and 480 grams?
The probability that a randomly chosen value is between 440 grams or 480 grams is _______.
(Round the probability to the nearest thousandths.)
How Many Standard Deviations From the Mean?
Use the Z-Score to find out.
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Question 4
4.
A study finds that the weights of infants at birth are normally distributed with a mean of 3270 grams and a standard deviation of 600 grams. An infant from the study is randomly chosen. What is the z-score for an infant that weighs 4170 grams?
Z-score = _______
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Question 5
5.
A study finds that the weights of infants at birth are normally distributed with a mean of 3270 grams and a standard deviation of 600 grams. An infant from the study is randomly chosen. What is the z-score for an infant that weighs 2790 grams?
Z-score = _______
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Question 6
6.
A study finds that the weights of infants at birth are normally distributed with a mean of 3270 grams and a standard deviation of 600 grams. An infant from the study is randomly chosen. What is the z-score for an infant that weighs 3990 grams?
Z-score = _______
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Question 7
7.
A data set has a normal distribution with a mean of 480 grams and a standard deviation of 20 grams. A value from the data set is randomly chosen. What is the probability that the value is 514 grams or less? Use the standard normal table.
The probability that a randomly chosen value is 514 grams or less is _______ (Round the probability to the nearest thousandths.)
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Question 8
8.
Parameter vs. Statistic
In your class, 27% of all students say that history is their favorite subject. Is this a parameter or a statistic?
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Question 9
9.
At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. What is the z-score for an order that is processed in 240 seconds?
Z-score = _______ (Round to the nearest hundredths)
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Question 10
10.
A data set has a normal distribution with a mean of 41 and a standard deviation of 6. About what percent of the data are between 41 and 100?
About _______ % of the data are between 41 and 100.
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Question 11
11.
A data set has a normal distribution with a mean of 41 and a standard deviation of 6. About what percent of the data are between 29 and 53?
About _______ % of the data are between 29 and 53.
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Question 12
12.
A data set has a normal distribution with a mean of 41 and a standard deviation of 6. About what percent of the data are between 35 and 47?
About _______ % of the data are between 35 and 47.
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Question 13
13.
A data set has a normal distribution with a mean of 41 and a standard deviation of 6. About what percent of the data are between 41 and 53?
About _______ % of the data are between 41 and 53.
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Question 14
14.
What is an example of confounding variable?
A confounding variable may distort or mask the effects of another variable on the disease in question.
For example, a hypothesis that coffee drinkers have more heart disease than non-coffee drinkers may be influenced by another factor.
What confounding variable could influence results?
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Question 15
15.
You want to study whether a low-carb diet can cause weight loss. What confounding variable could influence results? How can you adjust the study to prevent the influence?
Margin of Error and Confidence Intervals
A confidence interval is the mean of your estimate plus and minus the margin of error. This is the range of values you expect your estimate to fall between if you redo your test, within a certain level of confidence. Confidence, in statistics, is another way to describe probability.
Confidence intervals are most often constructed using confidence levels of 95% or 99%.
Calculating Confidence Intervals
Suppose a group of researchers is studying the heights of high school basketball players. The researchers take a random sample from the population and establish a mean height of 74 inches.
The mean of 74 inches is a point estimate of the population mean. A point estimate by itself is of limited usefulness because it does not reveal the uncertainty associated with the estimate; you do not have a good sense of how far away this 74-inch sample mean might be from the population mean.
At a 95% confidence level, researchers calculate a margin of error of ±2, plus and minus 2.
Add and subtract 2 from the sample mean, 74, to get the confidence interval: (72, 76)
We are 95% confident the true mean of all high school basketball player heights is between 72 and 76 inches.
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Question 16
16.
An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000 with a margin of error of ±$1,500.
Calculate the confidence interval for the true mean cost of repairing a car that experiences a 25 MPH head-on collision.
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Question 17
17.
A sample of 300 hundred eggs were randomly chosen from a female salmon and individually weighed. The mean weight was 0.978 grams with a margin of error of ± 0.005 grams.
Calculate the confidence interval for the true weight of salmon eggs.
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Question 18
18.
After completing a study of the rental cost for an unfurnished one-bedroom apartment in Atlanta, GA, we are 95% confident that the interval ($949.39, $1050.61) covers the true mean monthly rent of Atlanta apartments.
Calculate the sample mean.
Sample mean = _______
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Question 19
19.
Which of the following dot plots would most likely have the highest standard deviation?
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Question 20
20.
Two different cable company’s basic channel line up and number of customers are nearly identical but the companies vary in their pricing based on location.
Carter Cable charges customers a mean monthly price of $60 with a standard deviation of $14
Eighty & Tee cable charges customers a mean monthly price of $60 with a standard deviation of $5
Which of the following statement is most likely to be true?
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Question 21
21.
Use the Box-and-Whisker Plot to identify the third quartile, Q3.
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Question 22
22.
Consider the following Basic Box & Whisker Plot.
What is the Interquartile Range (IQR) of the data set shown in the graph?
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Question 23
23.
Which is the best definition of an Outlier?
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Question 24
24.
Consider the following Ordered Data Set.
2, 3, 5, 7, 7, 9, 10
Which is a correct box and whisker plot of the data above?
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Question 25
25.
Find the area between the z-scores,
z = 0 and z = 2.
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Question 26
26.
The D.O.T. collected data for a particular stretch of I-85 and found that the average speed was 70 mph with a standard deviation of 15 mph and the distribution is approximately normally distributed. The actual Speed Limit for the stretch of road is a maximum of 70 mph and minimum of 40 mph. What percentage of drivers actually drive between 40mph and 70 mph?
_______ % of drivers actually drive between 40mph and 70 mph?