Question

 It is reported that children between 2 and 6 years old watch an average of 20 hours of TV per week. Assume the variable is normally distributed and the standard deviation is 3 hours. If 20 children between the ages of 2 and 6 are randomly selected, find the probability that the mean of the number of hours they watch TV will be greater than 21.3 hours. 

Answer 1

Solution:

Given, $\mu=20,\sigma=3,n=20$

$X\sim N(\mu,\sigma) \\P(X>21.3)=1-P(X\le21.3) \\=1-P(z\le \dfrac{21.3-20}{3/\sqrt {20}}) \\=1-P(z\le 1.9379) \\=1-0.97381 \\=0.02619$