Question

Mandy has an IQ of 115. We know that the mean () IQ is 100 with a standard deviation of 15. There are 100 people in Mandy’s Alcoholics Anonymous meeting. Taken at random, how many members are smarter than Mandy

Answer 1

Answer: 16

Explanation:

Given : Mean :
`\mu=100`

Standard deviation :
`\sigma =15`

The value of z-score is given by :-

`z=(x-\mu)/(\sigma)`

For x= 115

`z=(115-100)/(15)=1`

The p-value :
`P(z>1)=1-P(z<1)=1- 0.8413447=0.1586553`

Now, the number of people smarter than Many is given by :_

`100*0.1586553=15.86553\approx16`

Hence, there are 16 members smarter than Mandy.