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 $60,000. A random sample of 43 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $ 57,500? Assume σ= $5,700.

The probability that the mean salary of the sample is less than ​$57,500 is

Answer 1

Solution :

Given that ,

mean = = 60000

standard deviation = = 5700

n = 43

= and 60000

= / n = 5700 / 43  = 869.24

P( < ) = P(( - ) / < (57500 - 60000) / 869.24)

= P(z < - 2.88 ) = 0.002

Using standard normal table,

Probability = 0.002