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 ​$60 comma 000. A random sample of 37 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than ​$57 comma 500​? Assume sigmaequals​$6 comma 300. The probability that the mean salary of the sample is less than ​$57 comma 500 is nothing. ​(Round to four decimal places as​ needed.)

Answer 1

Solution :

Given that ,

mean = = 60000

standard deviation = = 6300

n = 37

= 60000 and

= / n = 6300 / 37

P( < 57500) = P(( - ) / < (57500 - 60000) / 6300 / 37 )

= P(z < 2.41)

Using standard normal table,

= 0.992

Probability = 0.992