The heights of European 13-year-old boys can be approximated by a normal model w
ID: 2926699 • Letter: T
Question
The heights of European 13-year-old boys can be approximated by a normal model with mean of 63.2 inches and standard deviation of 2.56 inches. Question 1. 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 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 64.9 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 64.9 inches? (use 4 decimal places in your answer)Explanation / Answer
Mean is 63.2 and s is 2.56. z is defined as (x-mean)/s
a) P(x>64.9)= P(z>(64.9-63.2)/2.56)=P(z>0.66)=1-P(z<0.66) from normal distribution table it is 1-0.7454 =0.2546
b) P(xbar>64.9)=P(z>(64.9-63.2)/(2.56/sqrt(4)))=P(z>1.33) or 1-P(z<1.33) form normal distributtion table it is 1-0.9082=0.0918
c) P(xbar>64.9)=P(z>(64.9-63.2)/(2.56/sqrt(9)))=P(z>1.99) or 1-P(z<1.99)=1-0.9767 =0.0233
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