Question

In: Statistics and Probability

A random sample is drawn from a population with mean μ = 66 and a standard...

A random sample is drawn from a population with mean μ = 66 and a standard deviation σ =5.5.

Are the sampling distribution of the sample mean with n = 16 and with n = 36 normally distributed?

A. Yes, both the sample means will have a normal distribution.

B. No, for both sample sizes, the standard normal distribution could not be used.

C. No, the standard normal distribution could be used only for the sample size n = 16.

D. No, the standard normal distribution could be used only for the sample size n = 36.

Expert Solution

Solution :

Given that,

mean = = 66

standard deviation = = 5.5

n = 16

The sampling distribution of mean and standard deviation is ,

= 66 and

= / n = 5.5 / 16 = 5.5 / 4 = 1.375

n = 36

The sampling distribution of mean and standard deviation is ,

= 66 and

= / n = 5.5 / 36 = 5.5 / 6 = 0.9167

A. Yes, both the sample means will have a normal distribution.

orchestra answered 2 years ago

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