Estimating Mean When Sigma Is Known

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

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

• 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

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 , $\sigma_x$ = 11.547

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

• 5

• 0

In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval?

• 1084 to 1216 pounds 

• 1106 to 1150 pounds 

• 1106 to 1194 pounds 

• 1128 to 1172 pounds

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

•  28,000 km and 32,000 km.

• 24,000 km and 34,000 km.

• 26,000 km and 34,000 km.

• 27,000 km and 31,000 km.

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.

There are 500 golf members at the Mathy Country Club. How many are younger than 34?

• 16

• 80

• 100

• 150