In an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 5 inches. What percentage of the students are shorter than 76 inches tall, to the nearest tenth?

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Mathematics

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13 February, 23:14

In an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 5 inches. What percentage of the students are shorter than 76 inches tall, to the nearest tenth?

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Harper Shaw · Answer 1

15.87%

Step-by-step explanation:

First thing here is that we calculate the z-score which corresponds to 76

mathematically;

z-score = (x-mean) / SD

mean = 71 and SD = 5

plugging these values, we have;

z = (76-71) / 5 = 5/5 = 1

Now, we want to firstly get the probability that we have a student shorter than 76 inches

The probability we want to calculate is P (z<1)

we can get this using the z-score table directly

That would be 0.15866

In percentage that is 15.866% which is 15.87% to the nearest tenth