The heights of European 13-year-old boys can be approximated by a normal model w
ID: 3170829 • 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 65.3 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 65.3 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 65.3 inches? (use 4 decimal places in your answer) Question 4. True or false, the Central Limit Theorem was needed to answer questions 1, 2, and 3 above. Once I get to the part of (65.3-63.2)/ 2.26= 0.9292 and then 1-p(z less than or equal to 0.929) is when I get confused. Im not sure how others peoples examples got the correct answer because when I do the same problem to try to understand it, my z table score is different from theirs.
Explanation / Answer
mean =63.2
standard deviation =2.56 inches
1)
Convert x to z using z = (x-)/
=(65.3-63.2)/2.56
=0.8203
P(z>0.8203)=0.7939
the probability that the sample mean height x is taller than 65.3 inches is 0.7939.
2)
sample size=n=4
x¯ = / 4 = 2.56/2 = 1.28
Convert x to z using z = (x-)/
=(65.3-63.2)/1.28
=1.640
P(z>1.640)=0.9495
the probability that the sample mean height x is greater than 65.3 inches is 0.9495
3)
sample size=n=9
x¯ = / 9 = 2.56/3 = 0.853
Convert x to z using z = (x-)/
=(65.3-63.2)/0.853
=2.4618
P(z>2.4618)=0.9931
the probability that the sample mean height x is greater than 65.3 inches is 0.9931
4)
True , the Central Limit Theorem was needed to answer questions 1, 2, and 3 above for finding z value.
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