Question

A population of the IQ scores of 22,000 individuals is normally distributed with μ = 100...

A population of the IQ scores of 22,000 individuals is normally distributed with μ = 100 and σ = 15.

Suppose one individual is selected at random from this population and you had to guess the individual’s
IQ score within 13 points to win $1,000. What IQ score would you guess for the best chance of winning and what
would be the probability of winning the $1,000?

Math   Statistics-And-Probability   
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Answer #1

The mean IQ score would be most probable to occur as the individual's IQ score. And the scores more near to the mean would have higher probability than those far from the mean.

Thus, we would guess the IQ score as (100 - 6.5, 100 + 6.5) i.e. (93.5, 106.5) for the best chance of winning.

Let the IQ score be denoted by X

Probability of winning the $1000 = P(93.5 < X < 106.5)

= P( -0.433 < Z < 0.433)

(We converted the corresponding X values to Z score and will use the Z table to compute the probability)

= 0.3352

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