Question

The heights of European 13-year-old boys can be approximated by a normal model with mean μ of 63.1 inches and standard deviation σ of 2.32 inches.

Question 1. What is the probability that a randomly selected 13-year-old boy from Europe is taller than 65.7 inches? (use 4 decimal places in your answer)

Question 2. A random sample of 4 European 13-year-old boys is selected. What is the probability that the sample mean height x is greater than 65.7 inches? (use 4 decimal places in your answer)

Question 3. A random sample of 9 European 13-year-old boys is selected. What is the probability that the sample mean height x is greater than 65.7 inches? (use 4 decimal places in your answer)

Question 4. The Central Limit Theorem was needed to answer questions 1, 2, and 3 above. True False?

Answer 1

Here we transform sample mean (x bar ) to an approximately standard normal variable Z.

We can not use central limit theorem because sample size is less than 30.

Hence answer is false.