The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68 percent of the incomes lie between what two incomes?
a. $30,000 and $40,000
b. $36,400 and $38,000
c. $34,800 and $39,600
d. $35,600 and $38,800

Respuesta :

Answer:

Option B.

Step-by-step explanation:

Given information:

A group of middle management employees approximated a normal distribution.

Population mean [tex]\mu[/tex] = $37,200

Population standard deviation [tex]\sigma[/tex] = $800

About 68 percent of the incomes lie between two incomes and we need to find those two incomes.

We know that 68% data lies in the interval [tex][\mu-\sigma,\mu+\sigma][/tex].

[tex]\mu-\sigma=37,200-800=36,400[/tex]

[tex]\mu+\sigma=37,200+800=38,000[/tex]

About 68 percent of the incomes lie between what two incomes $36,400 and $38,000.

Therefore, the correct option is B.