Question

The mean weekly income of electrical engineers in NJ is $1,200 with a standard deviation of $200. If normally distributed, what percentages of workers earn more than $1,500?

Answer 1

Answer: 6.68%

Explanation:

Given : The mean weekly income of electrical engineers in NJ is $1,200 with a standard deviation of $200.

i.e.
`\mu=1200` and
`\sigma=200`

Let x denotes the monthly income ( in dollars).

If normally distributed , then the probability of workers earn more than $1,500 :

`P(x>1500)=1-P(\leq1500)\\\\=1-P((x-\mu)/(\sigma)\leq(1500-1200)/(200))\\\\=1-P(z\leq1.5)\ \ [\because\ z=(x-\mu)/(\sigma)]\\\\ =1-0.9332\ \ [\text{By z-table}]\\\\=0.0668=6.68\%`

Therefore , the percentages of workers earn more than $1,500 = 6.68%