In: Statistics and Probability
For a normal population with a mean equal to 81 and a standard deviation equal to 18, determine the probability of observing a sample mean of 87 or less from a sample of size 13.
Solution :
Given that,
mean =
= 81
standard deviation =
= 18
n = 13
= 81
=
/
n = 18
13 = 34.9923
p (
87 )
= 1 - P (
87 )
= 1 - P (
-
/
)
(87- 81 /4.9923)
= 1 - P( z
6 / 4.9923)
= 1 - P ( z
1.20 )
Using z table
= 1 - 0.8849
= 0.1151
Probability = 0.1151