Question

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.

Answer 1

Answer: 0.002718

Step-by-step explanation:

Given : The population mean annual salary for environmental compliance specialists is about ​$62,000.

i.e. $\mu=62000$  

Sample size : n= 32

$\sigma=6200$

Let x be the random variable that represents the annual salary for environmental compliance specialists.

Using formula $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$, the z-value corresponds to x= 59000 will be :

$z=\dfrac{59000-62000}{\dfrac{6200}{\sqrt{32}}}\approx\dfrac{-3000}{\dfrac{6200}{5.6568}}=-2.73716129032\approx-2.78$

Now, by using the standard normal z-table , the probability that the mean salary of the sample is less than ​$59,000 :-

$P(z$

Hence, the probability that the mean salary of the sample is less than ​$59,000= 0.002718