Question

A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 600 and 700

Answer 1

26.8% of examinees will score between 600 and 700.

This question is based on z score concept.

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

$z={x-\mu \over \sigma }$

where:

μ is the mean

σ is the standard deviation of the population

Given:

μ = 560

σ = 90

For

600≤ X≤700

for x = 700

Z score =x - μ/σ

=(700 - 560)/90

      = 1.55556

P-value from Z-Table:

P(560<x<700) = P(x<700) - 0.5 = 0.44009

for x = 600

Z score =x - μ/σ

=(600 - 560)/90

      = 0.44444

P-value from Z-Table:

P(560<x<600) = P(x<600) - 0.5 = 0.17164

∴ P(600<x<700) = P(560<x<700) - P(560<x<600)

                           = 0.44009 - 0.17164

                          =0.26845

∴26.8% percentage of examinees will score between 600 and 700.

Learn more about Z score here :

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