Module 3 Exercise 3

Which conditions hold true based on the central limit theorem? (Check all that apply.)

• If samples of size n = 30 are drawn from a population, then the sampling distribution of sample means approximate a normal distribution

• If samples of size n < 30 are drawn from a population, then the sampling distribution of sample means approximate a normal distribution

• If samples of size n > 30 are drawn from a population, then the sampling distribution of sample means approximate a normal distribution

• If samples of size n < 30 are drawn from a population which is normally distributed, then the sampling distribution of sample means is also normally distributed

Which properties apply if the sampling distribution of sample means is normally distributed? (Check all that apply.)

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Consider a population which is normally distributed. If

 $\mu=8.5$  , what is  $\mu_{\overline{x}}$  ? 

• 7

• 7.5

• 8

• 8.5

Consider a population which is normally distributed. If

 $\sigma^2=9$   and  $n=16$  , what is the variance of the sampling distribution of sample means? (Do not round off)

(a)  

Consider a population which is normally distributed. If

 $\sigma=2$  and  $n=9$  , what is the standard deviation of the sampling distribution of sample means?

• 0.67

• 0.22

• 0.44

• 1.33

Consider a population which is normally distributed. If

 $\mu_{\overline{x}}=2.75$  , what is  $\mu$  ?

(a)  

Cellular phone bills for residents of a city have a mean of P1,000 and a standard deviation of P170. Random samples of 100 cellular phone bills are drawn from this population and the mean of each sample is determined. Find the mean of the sampling distribution of sample means.

• 1000

• 170

• 100

• 17

Cellular phone bills for residents of a city have a mean of P1,000 and a standard deviation of P170. Random samples of 100 cellular phone bills are drawn from this population and the mean of each sample is determined. Find the standard deviation of the sampling distribution of the sample means.

(a)  

Suppose the training heart rates of all 20-year old athletes are normally distributed, with a mean of 135 beats per minute and standard deviation of 18 beats per minute. Random samples of size 4 are drawn from this population, and the mean of each sample is determined. Find the mean of the sampling distribution of sample means

• 135

• 18

• 4

• 20

Suppose the training heart rates of all 20-year old athletes are normally distributed, with a mean of 135 beats per minute and standard deviation of 18 beats per minute. Random samples of size 4 are drawn from this population, and the mean of each sample is determined. Find the variance of the sampling distribution of sample means

(a)