In engineering and product design, it is important to consider the weights of pe
ID: 2959308 • Letter: I
Question
In engineering and product design, it is important to consider the weights of people so that airplanes or elevators aren't overloaded. Based on data from the National Health Survey, assume the weight of adult males in the US follows a normal distribution with a mean weight of 170 pounds and standard deviation of 28 pounds.
c. If 9 different US adult males are randomly selected from the population above, what is the probability that their sample mean weight will be greater than 180 pounds? Give your answer to the nearest hundredth. Remember that probabilities are numbers between 0 and 1.
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d. If 36 different US adult males are randomly selected from the population above, what is the probability that their sample mean weight will be greater than 180 pounds? Give your answer to the nearest hundredth. Remember that probabilities are numbers between 0 and 1.
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Explanation / Answer
Given = 170, s=28
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c. Given n=9,
the probability that their sample mean weight will be greater than 180 pounds is
P(xbar > 180) = P((xbar-)/(s/n) >(180-170)/(28/3))
=P(Z>1.07)
= 0.1423 (check standard normal table)
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c. Given n=36,
the probability that their sample mean weight will be greater than 180 pounds is
P(xbar > 180) = P((xbar-)/(s/n) >(180-170)/(28/6))
=P(Z> 2.14)
= 0.0161 (check standard normal table)