Question

In an Arlington, NY school, the heights of the population of girls are normally distributed with a mean of 63 inches and a standard deviation of 2 inches. If there are 450 girls in the school, determine how many of the girls are shorter than 60 inches. Round the answer to the nearest integer

Answer 1

Number of girls shorter than
`60` inches are
`301`.

Explanation:

Given: The heights of the population of girls in an Arlington, NY school follows a normal distribution.

Mean
`=63`

Standard deviation
`=2`

Total number of girls
`=450`

Now using the formula,

Standard normal variant,
`z=(x-mean)/(standard deviation)`

Now, substitute the values and replace
`x` by
`60`

So.
`z=(60-63)/(2)`

`z=-(3)/(2)` or
`-1.5`

Now, probability of girls shorter than
`60` inches

`p(z>-1.5)=0.668` look up the value in the normal distribution table

Therefore, number of girls shorter than
`60` inches

`=0.668`×
`450`

`=301`