MATH SOLVE

2 months ago

Q:
# The population mean annual salary for environmental compliance specialists is about $62,000. A random sample of 32 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $59,000? Assume σ=$6,200.

Accepted Solution

A:

Answer: 0.002718Step-by-step explanation:Given : The population mean annual salary for environmental compliance specialists is about $62,000.i.e. [tex]\mu=62000[/tex] Sample size : n= 32[tex]\sigma=6200[/tex]Let x be the random variable that represents the annual salary for environmental compliance specialists.Using formula [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex], the z-value corresponds to x= 59000 will be :[tex]z=\dfrac{59000-62000}{\dfrac{6200}{\sqrt{32}}}\approx\dfrac{-3000}{\dfrac{6200}{5.6568}}=-2.73716129032\approx-2.78[/tex]Now, by using the standard normal z-table , the probability that the mean salary of the sample is less than $59,000 :-[tex]P(z<-2.78)=0.002718[/tex]Hence, the probability that the mean salary of the sample is less than $59,000= 0.002718