Population and Sample Mean

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

• It becomes narrower (less variability) and bimodal.

• It becomes narrower (less variability) and more normal.

• It becomes wider (more variability) and skewed right.

• It becomes wider (more variability) and more normal.

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population Distribution

• The Distribution of the Sample

• The Distribution of the Sample Means (Sampling Distribution)

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population Distribution

• The Distribution of the Sample

• The Distribution of the Sample Means (Sampling Distribution)

These symbols represent the mean and standard deviation for which of the following distributions?

• The Population Distribution

• The Distribution of the Sample

• The Distribution of the Sample Means (Sampling Distribution)

The mean of a population is μ = 200 the standard deviation is σ = 20. Random samples of size 25 are taken from this population.

What is the standard deviation of the sampling distribution?

• 200

• 16

• 25

• 4

• 5

• 0

• Approximately normal with  $\mu_x$  = 5.5 days and  $\sigma_x$ = 2.6 days

Answer explanation

The Central Limit Theorem kicks in here since the sample size is greater than 30. The sampling distribution would be skewed right for samples less than 30

The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons. What is the shape, mean and standard deviation of the distribution of sample means from samples of size n = 81.

• Normal,  $\mu_x$  = 4000,  $\sigma_x$  = 1.543

• Normal,  $\mu_x$  = 4000,  $\sigma_x$  = 13.89

• Normal,  $\mu_x$  = 444,  $\sigma_x$  = 13.89

Suppose the teenagers that attend public high schools get an average of 5.7 hours of sleep each night with a standard deviation of 1.7 hours. The distribution of sleep time is skewed to the left. What is the shape, mean, and standard deviation of the distribution of sample means from samples of size n = 400?

• Skewed Left, $\mu_x$ = 5.7 hours $\sigma_x$ = 0.085 hours

• Approximately Normal, $\mu_x$ = 5.7 hours $\sigma_x$ = 1.7 hours

• Skewed Left, $\mu_x$ = 5.7 hours $\sigma_x$ = 1.7 hours

Researchers found that boys playing high school football absorb an average of 355 hits to the head with a standard deviation of 80 hits during a season. If samples of 48 high school football players are randomly selected, what is the shape, mean and standard deviation of the distribution of sample means?

• Normal, $\mu_x$ = 355 , $\sigma_x$ = 11.547

• Approximately Normal, $\mu_x$ = 355 , $\sigma_x$ = 80

• Normal, $\mu_x$ = 355 , $\sigma_x$ = 80