Question

A random sample of size 36 is to be taken from a population that is normally distributed with mean 60 and standard deviation 18. The sample mean of the observations in our sample is to be computed. The sampling distribution of the sample mean is Select one: . a. normal with mean 36 and standard deviation 18. O b. normal with mean 60 and standard deviation 0.5. c. normal with mean 60 and standard deviation 3. d. normal with mean 60 and standard deviation 18.

Answer 1

Solution :

Given that ,

mean = $\mu$ = 60

standard deviation = $\sigma$ = 18

n = 36

$\mu$_{$\bar x$} = 60

$\sigma$_{$\bar x$} =$\sigma$  / $\sqrt$ n = 18/ $\sqrt$ 36=3

sampling distribution of the mean

$\mu$_{$\bar x$} = 60

sampling distribution of the standard deviation (standard error)

$\sigma$_{$\bar x$} =$\sigma$  / $\sqrt$ n = 18/ $\sqrt$ 36=3

correct option c normal with mean 60 and standard deviation 3