Normal Probability Sample Means

What happens to the shape of a sampling distribution of sample means as n increases?

• It becomes narrower (closer to the population's true mean) and bimodal.

• It becomes narrower (closer to the population's true mean) and more normal.

• It becomes wider (further from the population's true mean)and skewed right.

• It becomes wider (further to the population's true mean)and more normal.

In one region of the country, the mean length of stay in hospitals is 5.5 days with standard deviation 2.6 days. Because many patients stay in the hospital for considerably more days, the distribution of length of stay is strongly skewed to the right. Consider random samples of size 100 taken from the distribution with the mean length of stay, x, recorded for each sample. Which of the following is the best description of the sampling distribution of x ?

• Strongly skewed to the right with mean 5.5 days and standard deviation 2.6 days

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.26 day

• Strongly skewed to the right with mean 5.5 days and standard deviation 0.026 day

• Approximately normal with mean 5.5 days and standard deviation 2.6 days

• Approximately normal with mean 5.5 days and standard deviation 0.26 day

According to the Center for Disease Control, 93% of children entering kindergarten in the U.S. are vaccinated. A school district has 180 incoming kindergarten children.

Which of the following is true concerning the shape of the sampling distribution?

• The sampling distribution is normal because n > 30

• The sampling distribution is not normal because nq is < 30

• The sampling distribution is normal because 93% of 180 is > 10

• The sampling distribution is normal because np and nq are both > 10

What is the standard deviation of the distribution?

• 1010

• 20

• 60

• √20

According to government data, 22% of American children under the age of six live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 400 children. What is the probability that between 15% and 25% of children live in households with less than the official poverty level?

• 0.9998

• 0.0007

• 0.9259

• 1

• 0

A population has mean μ = 25 and standard deviation σ = 3.4. Find the mean and standard deviation of sampling distribution when n = 16.

• 25, 0.85

• 25, 3.4

• 6.25, 0.85

• 6.25, 3.4

62% of OHS students have plagiarized. Describe sampling distribution of size 30.

• Approximately normal with mean 0.62 and SD 0.0886

• Approximately normal with mean 62 and SD 8.86

• Approximately normal with mean 0.62 and SD 2.66

• The sample size is too small to determine shape.

What are the mean and standard deviation of the sampling distribution of sample means for an SRS of size 35?

• μx̅= 0.5 σx̅= 0.0488

• μ = 0.5 σ = 0.0488

• μx̅= 0.5 σx̅ = 0.289

• μ = 0.5 σ = 0.289

What is the probability a sample of 35 people will wait longer than 0.6 minutes for an elevator?

• 0.2018

• 0.9798

• 0.3632

• 0.0202

If the population of wait times was skewed, would that change your previous answer?

• No, the sample size is too small for the sampling distribution to be approximately Normal.

• No, the sample size is large enough for the sampling distribution to be approximately Normal.

• Yes, the sample size is too small for the sampling distribution to be approximately Normal.

• Yes, the sample size is large enough for the sampling distribution to be approximately Normal.