Answer to Question #324157 in Statistics and Probability for Ruth

Question

The ages of a certain group of students in a junior high school follow a normal

distribution with a mean of 13 and a standard deviation of 1.5. Find the probability

that a randomly selected student is between 10-16 years old.

Answer 1

mean =13

standard deviation=1.5

P(10<x<16)=P(z₂$\le$16)-P(z₁$\le$ 10)

z=$\frac{x-\mu}{\sigma }$

z₂= $\frac{16-13}{1.5}$

z₂=2

P(z₂$\le$ 2)=0.9772

z₁=$\frac{10-13}{1.5}$ =-2

P(z₁$\le$ -2)=0.0228

Thus

P(10<x<16)=0.9772-0.0228

P(10<x<16)=0.9544

The probability that a randomly selected student is between 10-16 years old is 0.9544.