Question

Heights of 10-year-olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. USE THE TI CALCULATOR FUNCTIONS TO COMPUTE YOUR ANSWER.What is the probability that a randomly chosen 10-year-old is shorter than 48 inches?

Answer 1

Probability that a randomly chosen 10-year-old is shorter than 48 inches 0.121 .

Explanation:

We are given that heights of 10-year-old closely follow a normal distribution with mean 55 inches and standard deviation 6 inches i.e.;

Mean,
`\mu` = 55 inches and Standard deviation,
`\sigma` = 6 inches

Also, Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

Let X = a randomly chosen 10-year-old

Now, Probability(X < 48 inches) = P(
`(X-\mu)/(\sigma)` <
`(48-55)/(6)` ) = P(Z < -1.17)

= 1 - P(Z < 1.17) = 1 - 0.87900 = 0.121

The above probability is calculated using z table.

Therefore, the probability that a randomly chosen 10-year-old is shorter than 48 inches is 0.121 .