A random variable X is not normally distributed. It has a mean of 41 and a standard deviation of 3.
List the givens with correct symbols:
μ = 41
σ = 3
a) If you take a sample of size 11, 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 normal
- σ is known
- σ is unknown
- population is not normal
- n is less than 30
- n is at least 30
b) For a sample of size 11, 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 = 11:
standard deviation of the sampling distribution of the sample mean when n = 11 rounded to two decimal places:
c) If you take a sample of size 38, can you say what the shape of the distribution of the sample mean is?
? No Yes
Why or why not?
- σ is known
- n is less than 30
- population is not normal
- σ is unknown
- n is at least 30
- population is normal
d) For a sample of size 38, 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 = 38:
standard deviation of the sampling distribution of the sample mean when n = 38 rounded to two decimal places: