Question

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?

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

It is assumed that individual IQ scores (denoted as X) are
normally distributed with mean (µ) and standard deviation (σ) given
as µ = 100 and σ = 15 Use normal table and conversion rule to
answer questions below.
1. Find proportion of individuals with IQ score below 109
2. Find a chance that a randomly selected respondent has the IQ
score above 103
3. What proportion of individuals would be within the interval
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4....

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What is the probability that a random sample of 20
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2) between 100 and 105?
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(can someone please show me how to answer this...i
keep mixing up my formulas ?)

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(c) Lower than 100?

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a. Determine the percentage of students who score between 85 and
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b. Determine the percentage of students who score 80 or
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