In: Statistics and Probability
The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.
For a sample of n=63 , find the probability of a sample mean being less than 19.8 if μ=20 and σ=1.33.
For a sample of n=63 , the probability of a sample mean being less than 19.8 if μ=20 and σ=1.33 is ______.
(Round to four decimal places as needed.)
Would the given sample mean be considered unusual?
The sample mean (would not/ would) be considered unusual because it has a probability that is (less/ greater) than 5%
Solution :
Given that ,
mean =
= 20
standard deviation =
= 1.33
n = 63
= 20 and
=
/
n = 1.33 /
63
= 0.16756
P(
< 19.8) = P((
-
) /
< (19.8 - 20) / 0.16756)
= P(z < -1.194)
= 0.1162
Probability = 0.1162
probability > 0.05
The sample mean would not be considered unusual because it has a probability that is greater than 5% .