Question

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 equals 63, find the probability of a sample mean being less than 20.2 if mu equals 20 and sigma equals 1.16.

Answer #1

Solution :

Given that ,

_{}
= 20

_{}
=
/
n = 1.16 /
63 = 0.146

P( < 20.2) = P(( -
_{}
) /
_{}
< (20.2 - 20) / 0.146)

= P(z < 1.37)

Using z table

= 0.9147

No, it would be not unusual because more than 5% of all such samples have means less than 20.2

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