Question

In an all boys school, the heights of the student body are normally distributedwith a mean of 71 inches and a standard deviation of 4.5 inches. Out of the1912 boys who go to that school, how many would be expected to be between61 and 70 inches tall, to the nearest whole number?

Answer 1

EXPLANATION

First, we need to apply the z-score table as shown as follows:

`z=(x-\mu)/(\sigma)`

Where u=mean=71 inches , standard deviation=sigma= 4.5 inches.

We need to compute the Probability that the student's height fall between 61 and 70 inches.

P(61

In terms of z-score this would be:

P(61

Computing the z-score when x=61:

`z=(61-71)/(4.5)=(-10)/(4.5)=-2.22`

Computing the z-score when x=70:

`z=(70-71)/(4.5)=(1)/(4.5)=-0.22`

Now we need to look up z= -2.22 and z=-0.22 on a z-table.

The results are z_-2.22= 0.01321 and z_-0.22=0.41294

Subtracting both terms give us the probability that the heights fall between those numbers: