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Sloan [31]
3 years ago
6

The salaries of Pet Detectives are normally distributed with a mean of $32,000 and a standard deviation of $3000. If 100 Pet Det

ectives are randomly selected, find the probability that their average salary is greater than $32,500. Select the single best answer choice
Mathematics
1 answer:
RideAnS [48]3 years ago
8 0

Answer:

P(\bar X> 32500)

And for this case we can use the z score formula given by:

z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing the info given we got:

z =\frac{32500-32000}{\frac{3000}{\sqrt{100}}}= 1.67

And for this case we can find the probability with the normal standard table using the complement rule and we got:

P(z> 1.67) = 1-P(z

Step-by-step explanation:

Let X the random variable that represent the salaries of Pet Detectives of a population, and for this case we know the distribution for X is given by:

X \sim N(32000,3000)  

Where \mu=32000 and \sigma=3000

We select a sample size of n =100 Pet Detectives and we want to find the following probability:

P(\bar X> 32500)

And for this case we can use the z score formula given by:

z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing the info given we got:

z =\frac{32500-32000}{\frac{3000}{\sqrt{100}}}= 1.67

And for this case we can find the probability with the normal standard table using the complement rule and we got:

P(z> 1.67) = 1-P(z

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