Question

in the country of united states of heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.8 inches, and standard deviation of 2.8 inches. what is the probability that the height of a randomly chosen child is between 52.9 and 55.6 inches? do not round until you get your your final answer, and then round to 3 decimal places.

Answer 1

The probability that the height of a randomly chosen child is between 52.9 and 55.6 inches will be 0.248

Given,

In the country of united states of heightlandia, the height measurements of ten-year-old children are approximately normally distributed

The mean of the distribution, μ = 53.8 inches

The standard deviation, σ = 2.8 inches

We have to find the probability that the height of a randomly chosen child is between 52.9 and 55.6 inches;

Here,

We want to find this probability:

P(52.9 < X < 55.6)

We can use the z score formula to solve this problem given by:

z score = (x - μ) / σ

Using this formula we have:

P(52.9 < X < 55.6) = P([52.9 - μ/σ] < X < [55.6 - μ/σ]) =

P((52.9 - 53.8/2.8) <  (x - μ) / σ < (55.6 - 53.8/2.8)) = P(-0.321 < z < 0.643)

And we can find this probability with this difference

P(-0.321 < z < 0.643) = P(z < 0.643) - P(z < -0.321)

We can use tables for the normal standard distribution, excel or a calculator and we got this;

P(-0.321 < z < 0.643) = P(z < 0.643) - P(z < -0.321) = 0.736 - 0.488 = 0.248

Therefore,

The probability that the height of a randomly chosen child is between 52.9 and 55.6 inches will be 0.248

Learn more about probability here;

https://brainly.com/question/16093880

#SPJ4