The heights of European 13-year-old boys can be approximated by a normal model w

Question

The heights of European 13-year-old boys can be approximated by a normal model with mean of 64.1 inches and standard deviation of 2.6 inches.

Question 1. What is the probability that a randomly selected 13-year-old boy from Europe is taller than 65.9 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 65.9 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 65.9 inches?

(use 4 decimal places in your answer)

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

TrueFalse   

Explanation / Answer

Mean is 64.1 and s is 2.6

a) P(x>65.9)=P(z>(x-mean)/s) or P(z>(65.9-64.1)/2.6)=P(z>0.69) or 1-P(z<0.69)

from normal distribution table we get 1-0.7549=0.2451

b) P(xbar>65.9)=P(z>(x-mean)/(s/sqrt(N))=P(z>(65.9-64.1)/(2.6/sqrt(4)) =P(z>1.38) =1-P(z<1.38)

from normal distribution table we get 1- 0.9162=0.0838

c) P(xbar>65.9)=P(z>(x-mean)/(s/sqrt(N))=P(z>(65.9-64.1)/(2.6/sqrt(9)) =P(z>2.07)=1-P(z<2.07)

thus answer is 1-0.9808=0.0192

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