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ki77a [65]
3 years ago
6

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.
Mathematics
1 answer:
lakkis [162]3 years ago
3 0

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

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