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 =70, find the probability of a sample mean being greater than 226 if μ=225 and sigma =5.8
Solution :
Given that ,
mean =
= 225
standard deviation =
= 5.8
=
/
n = 5.8 /
70 = 0.6932
P(
> 226) = 1 - P(
< 226)
= 1 - P[(
-
) /
< (226 - 225) / 0.6932]
= 1 - P(z < 1.44)
= 1 - 0.9251
= 0.0749
Probability = 0.0749
It is unusual because probability not unusual > 0.05