A random variable X is not normally distributed. It has a mean of 28 and a standard deviation of 7.

List the givens with correct symbols:

?

X

n

s

p

N

X

= 28

?

s

p

X

X

N

n

= 7

a) If you take a sample of size 15, can you say what the shape of the sampling distribution for the sample mean is?

?

No

Yes

Why or why not? Check all that apply.

• population is not normal
• is unknown
• is known
• n is less than 30
• n is at least 30
• population is normal

b) For a sample of size 15, state the mean and the standard deviation of the sampling distribution of the sample mean.

mean of the sampling distribution of the sample mean when n = 15:

standard deviation of the sampling distribution of the sample mean when n = 15 rounded to two decimal places:

c) If you take a sample of size 32, can you say what the shape of the distribution of the sample mean is?

?

No

Yes

Why or why not?

• is known
• is unknown
• population is normal
• n is at least 30
• population is not normal
• n is less than 30

d) For a sample of size 32, state the mean and the standard deviation of the sampling distribution of the sample mean.

mean of the sampling distribution of the sample meanwhen n = 32:

standard deviation of the sampling distribution of the sample mean when n = 32 rounded to two decimal places: