Answer: 82.30%
Step-by-step explanation:
Given : The starting salaries of individuals with an undergraduate degree from business schools are normally distributed with
[tex]\mu=\$44,000[/tex]
[tex]\sigma=\$4,000[/tex]
Let X be the random variable that represents the starting salaries of randomly selected individual with an undergraduate degree from business school.
Z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= $38,600
[tex]z=\dfrac{38600-44000}{4000}=-1.35[/tex]
For x= $49,400
[tex]z=\dfrac{49400-44000}{4000}=1.35[/tex]
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 :-
[tex]P(-135<z<1.35)=1-(2P(z<-1.35))\\\\=1-(2(0.088508))=0.822984\\\\\approx82.30\%[/tex]
