Normal and Skewed Distribution

What is the Normal Range (68%) of the annual precipitation for Phoenix, if the average is 29 with a standard deviation of 3?

• 26-32

• 3-29

• 26-29

• 39-32

Use the following information and the Empirical Rule to estimate the answer.

The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4.

Find the percentage of golfers that are between 30 and 46 years old.

• 68%

• 94%

• 95%

• 99.7%

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 mean of the sampling distribution?

• 200

• 16

• 25

• 4

• 50

• 25

• 20

• 5

The average speed of 1500 vehicles traveling on a stretch of highway one particular day is 67 miles per hour with a standard deviation of 3.5 miles per hour. If 100 vehicles are randomly selected as samples, what would be the mean of the resulting sampling distribution of sample means?

• 63.5

• 67

• 70.5

• 74

• 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

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