Answer to Question #181454 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 greater than 116 cm?

Answer 1

Z = (x - µ) / σ

Where,

x = 116 cm

µ = 110

σ = 6 cm

Z = (116 - 110) / 6

Z = 1

According to normal distribution table;

P (Z $\leq$ 1) = 0.8413

P (x > 116) = 1 - P (x < 116)

P (x > 116) = 1 - 0.8413

P (x > 116) = 0.1587

There is 15.87% probability that a child picked at random has a height greater than 116 cm.