Question

In: Statistics and Probability

IQ scores are standardized such that the population of scores has a mean of 100 and...

IQ scores are standardized such that the population of scores has a mean of 100 and a variance of 225. Assuming IQ scores have a normal distribution, what proportion of scores will fall below 80? What proportion will fall below 75?

What values occur in the top 9% of the distribution? What values occur in the bottom 9% of the distribution?

Solutions

Expert Solution

Suppose, random variable X denotes IQ score.

(a)

Corresponding probability is given by

[Using R-code 'pnorm(-1.333333)']

Hence, 0.09121127 proportion of scores will fall below 80.

(b)

Corresponding probability is given by

[Using R-code 'pnorm(-1.666667)']

Hence, 0.04779032 proportion of scores will fall below 75.

(c)

We have to find so that

[Using R-code 'qnorm(1-0.09)']

Hence, values higher than 120.1113 occur in the top 9% of the distribution.

(d)

We have to find so that

[Using R-code 'qnorm(0.09)']

Hence, values lower than 79.8887 occur in the bottom 9% of the distribution.

orchestra answered 1 year ago

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