Question

The heights of the children at a summer camp are normally distributed with a mean of 58 in. and a standard deviation of 4 in.

There are 150 children at the summer camp.

About how many children are expected to have heights between 54 in. and 62 in.?



51

71

102

143

Answer 1

First, we must find the z-scores for each limit
for 54
z = (54 - 58) / 4 = -1
For this z-score, the area under the curve is 0.1587

for 62
z = (62 - 58) / 4 = 1
The area under the curve is 0.8413

Subtracting the two z-scores:
0.8413 - 0.1587 = 0.6825

Multiplying by 150
150 (0.6825) = 102.39

So, the closest answer is
102