Lessons 6.3 - 6.4 Practice (due 3/18) - WENDY NOSAL | Library

Instructions

This is a grade for the 4th 9 weeks.

Required

2

Lesson 6.3
Dysplasia is a malformation of the hip socket that is very common in certain dog breeds and causes arthritis as a dog gets older.  According to the Orthopedic Foundation for Animals, 11.6% of all Labrador retrievers have hip dysplasia.
A veterinarian tests a random sample of 50 Labrador retrievers and records 
Y = the proportion of Labs with dysplasia in the sample.

a. What is the mean of the sampling distribution of Y?  _______ 
b. What is the standard deviation of the sampling distribution of Y? _______ round to three places past the decimal.

Required

2

Lesson 6.3:
Interpret the standard deviation from #1:
Make sure to check your notes.
I will grade this question by hand.

Required

4

Lesson 6.3
Would it be appropriate to use a normal distribution to model the sampling distribution
of Y = the number of Labs with dysplasia in the sample?
Check the Large Counts Condition.
Justify your answer.

Select the four answers that explain.

Required

2

Lesson 6.3:
In a congressional district, 55% of registered voters are Democrats. A polling organization selects a random sample of 500 registered voters from this district. 
Let  x= the proportion of Democrats in the sample.

1. Calculate the mean proportion of the sampling distribution of the proportion of Democrats in the sample (x): _______ 
Enter your answer as a decimal rounded to two places.

2. Calculate the standard deviation of the sampling distribution of x: _______ 
    Round to three places past the decimal.

Required

4

Lesson 6.3:
In a congressional district, 55% of registered voters are Democrats. A polling organization selects a random sample of 500 registered voters from this district.
Let x= the proportion of Democrats in the sample.

Would it be appropriate to use the Normal Distribution with the above situation?
Hint: is the Large Counts Condition met?
Select the four answers that explain.

Required

2

Lesson 6.3:
Since it is appropriate to use the Normal Distribution for the scenario below:
In a congressional district, 55% of registered voters are Democrats. A polling organization selects a random sample of 500 registered voters from this district.
Let  x= the proportion of Democrats in the sample.

What is the probability that not more than 59.6% of a sample of 500 registered voters are Democrats? _______ 
Use the Normal Distribution calculations we learned in Ch. 5 (hint: z score & blue chart). Keep all four decimal places.

What is the probability that at least 57% of the registered voters are Democrats? _______ 

Required

2

A USA Today poll asked a random sample of 1012 U.S. adults what they do with the milk in their cereal bowl after they have eaten. 
Let p-hat be the proportion of people in the sample who drink the cereal milk. 
A spokesman for the dairy industry claims that 70% of all U.S. adults drink the cereal milk. Suppose this claim is true.
a. What is the mean of the sampling distribution for p-hat? _______ 
b. What is the standard deviation of the sampling distribution for p-hat? _______ Round to three places past the decimal.

Required

4

Lesson 6.3:
A USA Today poll asked a random sample of 1012 U.S. adults what they do with the milk in their cereal bowl after they have eaten.
Let p-hat be the proportion of people in the sample who drink the cereal milk.
A spokesman for the dairy industry claims that 70% of all U.S. adults drink the cereal milk. Suppose this claim is true.

Would it be appropriate to use the Normal Distribution with the above situation?
Hint: is the Large Counts Condition met?
Select the four answers that explain.

Required

4

Lesson 6.3: Testing a Claim
Of the poll respondents, 67% said that they drink the cereal milk. Based on your answer to #8, does this poll give convincing evidence that less than 70% of all U.S. adults drink the cereal milk?
Explain by finding the probability that 67% would drink the cereal milk then decide if this is unusual or not.
Hint: use the Normal Distribution calculations from Ch. 5

Required

2

Lesson 6.4:
Driving styles differ, so there is variability in the fuel efficiency of the same model automobile driven by different people. For a certain car model, the mean fuel efficiency is 23.6 miles per gallon with a standard deviation of 2.5 miles per gallon.
Take a simple random sample of 25 owners of this model and calculate the sample mean fuel efficiency .

1. What is the mean of the sampling distribution of sample means: _______ 
Do not include units.

2. Calculate the standard deviation of the sampling distribution of sample means: _______ 

Required

3

Lesson 6.4:
One dimension of bird beaks is “depth”—the height of the beak where it arises from the bird’s head. 
During a research study on one island in the Galapagos archipelago, the beak depth of all Medium Ground Finches on the island was found to be normally distributed with mean 
μ = 9.5 millimeters and standard deviation σ = 1.0 millimeter.
A sample of 10 randomly selected Medium Ground Finches as collected and their beaks measured.
1. What is n? _______ 
2. What is the mean of the sampling distribution? _______ 
3. What is the standard deviation of the sampling distribution of sample means? _______ 
Round your answer to three places past the decimal.

Required

2

Lesson 6.4:
Interpret the Sampling Distribution Standard Deviation of beak depths below:
(I will grade this myself)

Required

3

Lesson 6.4:
Using the information on beak depths above:
What is the Normal Model notation for our sampling distribution of the sample means? _______ 

What is the probability that a sample of 10 finches will have a mean beak length that is less than 9 millimeters deep? _______ 
Keep all four decimal places.

What is the probability that the mean beak depth in 10 randomly selected Medium Ground Finches is at least 10.2 millimeters? _______ 
Keep all four decimal places.

Required

1

Lesson 6.4:
How large would the sample size need to be to have a standard deviation of 0.25 instead of 0.316 for the sampling distribution of sample means for beak depth?
Remember, the population standard deviation = 1.0 mm.
Use the standard deviation formula, set it up to solve for the sample size (n).
** Use your algebra skills to solve for n!!

Required

4

Lesson 6.4:
An automaker has found that the lifetime of its batteries varies from car to car according to a normal distribution with mean μ = 48 months and standard deviation σ = 8.2 months. 
The company installs a new battery on an SRS of 8 cars.

1. What is the sample size?  _______ 
2. What letter stands for the sample size?  _______  (remember it is lower case)

3. What is the mean of the sampling distribution of sample means for battery lifetime? _______  do not include units

4. What is the standard deviation of the sampling distribution of the sample means for battery lifetime? _______ 
Round to three places past the decimal.

Required

3

Lesson 6.4:
Using the information on battery lifetime sampling distribution:
What is the Normal Model for this scenario? _______ 

Find the probability that the sample mean battery life is less than 42.4 months:  _______ 
Keep all four decimal places.

Find the probability that the sample mean battery life is more than 45 months: _______ 
Keep all four decimal places.

Required

1

Lesson 6.4:
How large of a sample size would be needed to decrease the standard deviation from 2.899 to 1.5 for battery lifetime?
Remember the population standard deviation = 8.2 months.
Set up the formula for the standard deviation, use your algebra skills to solve for n!
Round to the nearest whole.

Required

3

A company’s cereal boxes advertise that 9.65 ounces of cereal are contained in each box. In fact, the amount of cereal in a randomly selected box follows a normal distribution with mean μ = 9.70 ounces and standard deviation σ = 0.04 ounce. 
What is the probability that the mean amount of cereal  in 5 randomly selected boxes is at least 9.65?
a.  n=_______ 
b. standard deviation for the sampling distribution = _______ 
c. What is the probability that the cereal boxes contain at least 9.65 ounces? _______ 

Lessons 6.3 - 6.4 Practice (due 3/18)

Lessons 6.3 - 6.4 Practice (due 3/18)

Lesson 6.3:Interpret the standard deviation from #1: Make sure to check your notes.I will grade this question by hand.

Lesson 6.3Would it be appropriate to use a normal distribution to model the sampling distributionof Y = the number of Labs with dysplasia in the sample?Check the Large Counts Condition.Justify your answer.Select the four answers that explain.

Lesson 6.4:Interpret the Sampling Distribution Standard Deviation of beak depths below:(I will grade this myself)

Lesson 6.4:How large of a sample size would be needed to decrease the standard deviation from 2.899 to 1.5 for battery lifetime? Remember the population standard deviation = 8.2 months.Set up the formula for the standard deviation, use your algebra skills to solve for n!Round to the nearest whole.

Lesson 6.3:Interpret the standard deviation from #1: Make sure to check your notes.I will grade this question by hand.

Lesson 6.3Would it be appropriate to use a normal distribution to model the sampling distributionof Y = the number of Labs with dysplasia in the sample?Check the Large Counts Condition.Justify your answer.Select the four answers that explain.

Lesson 6.4:Interpret the Sampling Distribution Standard Deviation of beak depths below:(I will grade this myself)

Lesson 6.4:How large of a sample size would be needed to decrease the standard deviation from 2.899 to 1.5 for battery lifetime? Remember the population standard deviation = 8.2 months.Set up the formula for the standard deviation, use your algebra skills to solve for n!Round to the nearest whole.

Lesson 6.3:
Interpret the standard deviation from #1:
Make sure to check your notes.
I will grade this question by hand.

Lesson 6.3
Would it be appropriate to use a normal distribution to model the sampling distribution
of Y = the number of Labs with dysplasia in the sample?
Check the Large Counts Condition.
Justify your answer.

Select the four answers that explain.

Lesson 6.4:
Interpret the Sampling Distribution Standard Deviation of beak depths below:
(I will grade this myself)

Lesson 6.3:
Interpret the standard deviation from #1:
Make sure to check your notes.
I will grade this question by hand.

Lesson 6.3
Would it be appropriate to use a normal distribution to model the sampling distribution
of Y = the number of Labs with dysplasia in the sample?
Check the Large Counts Condition.
Justify your answer.

Select the four answers that explain.

Lesson 6.4:
Interpret the Sampling Distribution Standard Deviation of beak depths below:
(I will grade this myself)