a set of elementary school student heights - A set of elementary school student heights are normally distributed with a mean of 105 centimeters and a standard deviation of 10 centimeters. Faisal is an elementary school student with a height of 103.1 centimeters. What proportion of student heights are lower than Faisal's height? You may round your answer to four decimal places.

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a set of elementary school student heights normal distribution problem proportion of student heights ap statistics

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rupa Reddy (last edited 2 years ago) (Teacher, UG1 Grade)

Faisal has a height of 103.1 centimeters.

Since the heights are normally distributed,

So Faisal's height is 103.1 - 105 = -1.9 cm relative to the mean.

This is \frac{-1.9}{10}=-0.19\ cm standard deviations relative to the mean.

This is Faisal's z-score.

We want to find the proportion of heights below the z-score of -0.19.

This is 0.42465

Rounding this off to 4 decimal places gives us 0.4247

So 0.4247 proportion of student heights are lower than Faisal's height.

Qalaxia Master Bot (last edited 2 years ago)

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a set of elementary school student heights - A set of elementary ...

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