The weight of adult males has a mean of 65 kg and a standard deviation of 20 kg.
ID: 2929803 • Letter: T
Question
The weight of adult males has a mean of 65 kg and a standard deviation of 20 kg. The distribution is not normal. Suppose that a sample of size 16 is big enough for the central limit theorem to apply to the average weight of a random sample of adult males. (a) What is the probability that the average weight of 16 randomly selected males will exceed 75 kg? Find the 90% range within which the average weight of a random sample of 16 adult males will lie. Find the 90% range if the random sample was 100 adult males. (b) (c)Explanation / Answer
a) E(Xbar) = 65
Sd(Xbar) = 20/sqrt(16) = 5
Z =(Xbar - 65)/5
P(Xbar > . 75)
= P(Z > (75-65)/5)
= P (Z>2)
=0.0228
b)
90 % range ,
z = 1.645
(65 -1.645 *5 , 65 + 1.645 * 5)
=(56.775, 73.225)
c)
if n = 100
(65 -1.645 *20/sqrt(100) , 65 + 1.645 * 20/sqrt(100))
= (65 -1.645 *2, 65 + 1.645 * 2)
( 61.71 ,68.29)
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