Question

A normal population has a mean of 65 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is:

Answer 1

QUESTION: A normal population has a mean of 65 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is:

a. Greater than 67

b. Less than 64

c. Between 64 and 67

SOLUTION:

GIVEN: Mean, =65; Std deviation, =13; Sample size, n =16; Let P= Probability.

a.

=67

Z = = =0.615

P( X>67) =P(Z>0.615) =0.5 - 0.23 =0.27

b.

=64

= = - 0.308

P(X<64) =P(Z< - 0.308) =0.5 - 0.12 =0.38

c.

P(between 64 and 65) =P(​​​​​​) =P(-0.3080.615) =0.12 +0.23 =0.35