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

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

The probability $P(X$ is calculated after converting the raw score to the standard score,

$P(X$.

Now use normal distribution table or technology,

$P(X$.

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 $2,083$.

Answer 2

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