Question

from a survey taken several years ago, the starting salaries of individuals with an undergraduate degree from business schools are normally distributed with a mean of $44,000 and a standard deviation of $4,000. what percentage of individuals with an undergraduate degree will likely have starting salaries of $38,600.00 to $49,400.00

Answer 1

Answer: 82.30%

Explanation:

Given : The starting salaries of individuals with an undergraduate degree from business schools are normally distributed with

`\mu=\$44,000`

`\sigma=\$4,000`

Let X be the random variable that represents the starting salaries of randomly selected individual with an undergraduate degree from business school.

Z-score :
`z=(x-\mu)/(\sigma)`

For x= $38,600

`z=(38600-44000)/(4000)=-1.35`

For x= $49,400

`z=(49400-44000)/(4000)=1.35`

Using the standard normal table , the probability of individuals with an undergraduate degree will likely have starting salaries of $38,600.00 to $49,400.00 will be :-

`P(-135<z<1.35)=1-(2P(z<-1.35))\\\\=1-(2(0.088508))=0.822984\\\\\approx82.30\%`