Aset of elementary school student heights are normally distributed with a mean of 105105105 centimeters and a standard deviation of 777 centimeters. what proportion of student heights are between 94.594.594, point, 5 centimeters and 115.5115.5115, point, 5 centimeters? you may round your answer to four decimal places.

Using the normal distribution, it is found that the proportion of student heights are between 94.5 centimetres and 115.5 centimetres is of 0.8664.

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Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation , the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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X = 115.5

has a p-value of 0.9332.

X = 94.5

has a p-value of 0.0668.

0.9332 - 0.0668 = 0.8664.

The proportion of student heights are between 94.5 centimetres and 115.5 centimetres is of 0.8664.

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