Answer to Question #181448 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 fewer than 95 cm or more than 130 cm?

Answer 1

Let's find the probability that a child has a height taller than 95 cm and less than 130 cm (P). Then the probability that a child picked at random has a height fewer than 95 cm or more than 130 cm (P') = 1 - P.

The probability that 95 < X < 130 is equal to the blue area under the curve.

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

P( 95 < X < 130) =  P(95 - 110 < X - $\mu$ < 130 - 110) = P$(\frac{95-110}{6} < \frac{X-\mu}{\mu} < \frac{130-110}{6} )$

Since $Z = \frac{X-\mu}{\sigma}, \ \frac{95-110}{6} = -2.5$ and $\frac{130-110}{6} = 3.33$ we have:

P( 95 < X < 130) = P(-2.5 < Z < 3.33)

Use the standard normal table to conclude that:

P(-2.5 < Z < 3.33) = 0.9934

Than, P' = 1 - 0.9934 = 0.0066

Answer: P' = 0.0066.

P.S. Here's the standard normal table: