Answer to Question #181452 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. How many children have heights between 98 cm and 104 cm?

Answer 1

mean $= \mu = 110$

standard deviation $= \sigma = 6$

$P(98<x<104) = P(\frac{98-110}{6}<Z< \frac{104-110}{6}) \\ = P(-2 <Z< -1) \\ = P(Z< -1) -P(Z< -2) \\ = 0.1586 – 0.0227 \\ = 0.1359$

= 13.59 %

$500 \times 0.1359 = 68$ children have heights between 98 cm and 104 cm