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Lessons 6.3 - 6.4 Practice (due 3/18)

Last updated over 1 year ago
18 questions
Note from the author:
This is a grade for the 4th 9 weeks.
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.
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Lesson 6.3:
Interpret the standard deviation from #1:
Make sure to check your notes.
I will grade this question by hand.

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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? _______
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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

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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: _______
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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.
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2

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

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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.
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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!!

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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.

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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? _______