Question

The mean hourly income of midwives in NJ is $55 with standard deviation of $15. Given that the distribution is normal, what percentage of NJ midwives earn more than $60 per hour?

A.10%
B.25%
C.70%
D.none of the above

Answer 1

Answer: D. none of the above

Explanation:

Let x = a random variable that denotes the hourly income of midwives.

As per given , we have

`\mu=\$55`

`\sigma=\$15`

Also, the distribution is normal.

Then, the probability that NJ midwives earn more than $60 per hour will be :_

`P(x>60)=1-P(x<60)=1-P((x-\mu)/(\sigma)<(60-55)/(15))\\\\=1-P(z<0.33)\ \ [\because\ z=(x-\mu)/(\sigma)]\\\\=1-0.6293\ \ [\text{By z-table}]\\\\ =0.3707=37.07\%`

Hence, the percentage of NJ midwives earn more than $60 per hour is approximately 37.07%.

Since , 37.07% is not given in any option.

So the correct answer to this question is "D.none of the above"