Use the normal distribution of IQ scores, which has a mean of 95 and a standard

Question

Use the normal distribution of IQ scores, which has a mean of 95 and a standard deviation of 13, and the following table with the standard scores and percentiles for a normal distribution to find the indicated quantity.

The percentage of scores between 62.5 and 108 is _____%.

(Round to two decimal places as needed.)

Standard score Percent -3.0 0.13 -2.5 0.62 -2 2.28 -1.5 6.68 -1 15.87 -0.9 18.41 -0.5 30.85 -0.1 46.02 0 50.00 0.10 53.98 0.5 69.15 0.9 81.59 1 84.13 1.5 93.32 2 97.72 2.5 99.38 3 99.87 3.5 99.98

Explanation / Answer

X lies between 62.5 and 108

Convert these scores to Z scores

mu = 95 and sigma = 13

For 62.5, z = -32.5/13 = -2/5

For 108, z score = +13/13 = 1

Hence percentage of scores lying between

(-2.5<z<1) = 0.4938+0.3413

= 0.8351

= 83.51%

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