Answer to Question #181455 in Statistics and Probability for Alice

Question

Five hundred children participated in a field demonstration. Their heights averaged is 110 cm with a standard deviation of 6 cm. What is the probability that a child picked at random has a height less than 104 cm?

Answer 1

We assume normal distribution with the mean ($\mu$ ) and standard deviation ($\sigma$ ) which are given as follows

$$\mu =110 \text{ cm and } \sigma =6\text{ cm }.$$

Therefore,

$$P (x < 104 ) = P (z<\frac{x-\bar{\mu}}{\sigma})=P(z<\frac{104-110}{6}),\\ =P(z<\frac{-6}{6})=P(z<-1)=0.15866.$$

Thus, the probability that a child picked at random has a height less than 104 cm is 0.15866.