Engineers must consider the breadths of male heads when designing motorcycle hel
ID: 3384073 • Letter: E
Question
Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.5 inches and a standard deviation of 1.1 inches. (a) If one male is randomly selected, find the probability that his head breadth is less than 5.9 inches. (b) If a random sample of 64 males is selected, find the probability that the mean of their head breadths is less than 6.1 inches. (c) Is there a difference in the two answers? Explain your answer.
Explanation / Answer
Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.5 inches and a standard deviation of 1.1 inches.
(a) If one male is randomly selected, find the probability that his head breadth is less than 5.9 inches.
Z value for 5.9, z=(5.9-6.5)/1.1 =-0.55
P( x < 5.9) = P( z< -0.55) = 0.2912
(b) If a random sample of 64 males is selected, find the probability that the mean of their head breadths is less than 6.1 inches.
Standard error = sd/sqrt(n) =1.1/sqrt(64) =0.1375
Z value for 6.1, z=(6.1-6.5)/0.1375 =-2.91
P( x < 6.1) = P( z< -2.91)
= 0.0018
(c) Is there a difference in the two answers? Explain your answer.
Yes, there is a difference in the two answers. In the first, individual value is used. In the second, mean value is used and for this we calculated standrd error of the mean.
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