Question

the height measurements of ten-year-old children are approximately normally distributed with a mean of 54.1 inches, and standard deviation of 2.7 inches. A) What is the probability that a randomly chosen child has a height of less than 51.85 inches?

Answer 1

The probability that a randomly chosen child has a height of less than 51.85 inches is 0.2033

Explanation:

Mean = 54.1 inches

Standard deviation = 2.7 inches

We are supposed to find the probability that a randomly chosen child has a height of less than 51.85 inches

P(x<51.85)

Formula :
`Z=(x-\mu)/(\sigma)`

Substitute the values in the formula :

`Z=(x-\mu)/(\sigma)`

`Z=(51.85-54.1 )/(2.7)`

`Z=-0.83`

Refer the z table for p value

p value = 0.2033

Hence the probability that a randomly chosen child has a height of less than 51.85 inches is 0.2033