Question

What is the probability that the height of a child, picked at random, is less than 104 cm?

Answer 1

Five hundred children participated in a field demonstration. Their heights averaged 110

cm with a standard deviation of 6 cm.

The probability that X<104 is equal to the blue area under the curve.

Since $\mu=110$  and $\sigma=6$  we have:

$P(X<104) = P(X-\mu<104-110)=P(\frac{X-\mu}{\sigma}<\frac{104-110}{6})$

Since 

$\frac{x-\mu}{\sigma} = Z$  and $\frac{104-110}{6} = -1$

 we have:

$P(X<104)=P(Z<-1)$

Use the standard normal table to conclude that:

$P(Z<-1)=0.1587$

Answer: 0.1587.