Answer to Question #210934 in Statistics and Probability for mila

Question

Five hundred children participated in a field demonstration.Their heights averaged 110 cm with a standard deviation of 6 cm.How many children , picked at random,has a height greater than 116 cm?

Answer 1

$N=500 \\ \mu=110 \\ \sigma=6 \\ P(X>116) = 1 -P(X<116) \\ = 1 - P(Z< \frac{116-110}{6}) \\ = 1- P(Z<1) \\ = 1 -0.3413 \\ = 0.8413$

Number of children, which heights greater than 116 cm =

$= 0.8413 \times 500 \\ = 421$