Question

Find the probability and interpret the results. If​ convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about ​$64,500. A random sample of 33 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than ​$61,500​? Assume sigma= ​$5,500. The probability that the mean salary of the sample is less than ​$61,500 is . ​(Round to four decimal places as​ needed

Answer 1

Solution:

Given that,

mean =  = 64500

standard deviation =   =   5500

n = 33

= 64500

=  ( /n) = (5500 / 33 ) = 957.4271

p (   < 61500 )

= p ( - /) < ( 61500 - 64500 / 957.4271 )

= p ( z < - 3000 / 957.4271 )

= p ( z < - 3.13 )

Using z table

= 0.0009

Probability = 0.0009,