Question

A standard I.Q. test produces normally distributed results with a mean of 104 and a standard deviation of 16 for 52,000 students in grade 12 in the province. Approximately how many of these people would have I.Q.s below 76?

4,170

23,915

2,127

2,083

Answer 1

I'm looking for this aswell

Answer 2

The IQ scores are RVs (X) normally distributed with mean
`\mu=104` and standard deviation
`\sigma =16`.

The probability
`P(X<76)` is calculated after converting the raw score to the standard score,

`image`.

Now use normal distribution table or technology,

`P(X<76)=\Phi(-1.75) =0.0401`.

Thus, the number of people who would have I.Q.s below 76 out of 52,000 is

`0.0401*52000=2,085.2`.

Therefore, the approximate number is
`2,083`.