approximately normally distributed with a mean of 53.6 inches, and standard deviation of 2.2 inches.

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 53.6 inches, and standard deviation of 2.2 inches.

A.) What is the probability that a randomly chosen child has a height of less than 56.3 inches ?

B.) What is the probability that a randomly chosen child has a height of more than 52.5 inches ?

Answer 1

Part A: You need to find the following probability: P(X)< 56.3.

First, you need to convert this to a standard normal variable by using the information they give (i.e. mean and std, dev.). By converting the variable(X) to a std. normal variable(Z), you can use the tables that are likely in the back of your book to determine the P(Z)< (56.3-53.6)/2.2. You'll need to look to see what probability the table in your book gives, as there are different versions of the tables. Some give the probability to the left of a value, while others give the probability to the right of the variable

**Notice: you need to standardize both sides of the equation!

Part B) You need to find the following Probability: P(X) >52.5. Follow the same procedure as above: Standardize both sides, then look up the probability in the tables (unless you can use a calculator or have assess to software that can do it for you.