sample mean value

Question

You are told that a variable X follows a normal model with µ = 9.1 with σ = 0.3.

If random samples of size 75 are chosen from the population, what is the sample mean value that has 1.5% of all sample mean values beneath it?

Please give your answer correctly rounded to two decimal places.

Answer 1

The sample means will have a normal distribution, mean 9.1, standard deviation 0.3 / √75

You need to find a so that p (X<a) = 1.5% = 0.015

If you have a Z/ area table, find the value of Z corresponding to an area of 0.015 in the table.

Then Z = (X - 9.1) / (0.3 / √75) using the definition of Z, and you can solve this for X.

Alternatively, on a TI-84

2nd vars

invnorm

area = 0.015

mean = 9.1

sd = 0.3 / √75

giving 9.02 as the answer