Question

The heights of European 13-year-old boys can be approximated by a normal model with mean μ of 64.2 inches and standard deviation σ of 2.37 inches.

Question B1. What is the probability that a randomly selected 13-year-old boy from Europe is taller than 64.9 inches? (use 4 decimal places in your answer)

Question B2. 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 64.9 inches? (use 4 decimal places in your answer)

Question B3. 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 64.9 inches? (use 4 decimal places in your answer)

Question B4. The Central Limit Theorem was needed to answer questions 1, 2, and 3 above. True or False

Answer 1

B1)

                                   

                                    = P(Z > 0.30)

                                    = 1 - P(Z < 0.3)

                                    = 1 - 0.6179

                                    = 0.3821

B2) n = 4

                            

                             = P(Z > 0.59)

                             = 1 - P(Z < 0.59)

                             = 1 - 0.7224

                             = 0.2776

B3) n = 9

                            

                             = P(Z > 0.89)

                             = 1 - P(Z < 0.89)

                             = 1 - 0.8133

                             = 0.1867

B4) Option-B) False. Because the main population is normally distributed so the sampling distribution will also be normally distributed