Question

Suppose nine items are sampled from a normally distributed population with a mean of 108 and a standard deviation of 16 . The nine randomly sampled values are shown in the table. 134, 85, 85, 124, 111, 107, 131, 70 ,133.

Calculate the probability of getting a sample mean that is smaller than the mean for these nine sampled values. The probability that a sample mean is smaller than the mean for these nine values is ___ . (Round to four decimal places as needed.)

Answer 1

Solution:

Let  

n= 9 random sample

sample mean .

To find

. By using central limit theorem

= P ( Z < 0.1668750)

= P ( Z < 0.17)

= 0.5675 From Z table

The probability that a sample mean is smaller than the mean for these nine values is 0.5675.