SOLUTION: Question No. 9 The weights of a certain population of pregnant women are approximately normally distributed with a mean of 62 kilogram and a standard deviation of 16. Find the pro

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Question 1151901: Question No. 9
The weights of a certain population of pregnant women are approximately normally distributed with a mean of 62 kilogram and a standard deviation of 16. Find the probability that 16 women selected at random from this population will have the mean weight between 45 and 75 kilogram and interpret the result
Answer by Boreal(15235) (Show Source):
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for the mean weight, z= (mean of sample- mu)/sigma/sqrt(n)
for 45 z=(45-62)/16/sqrt(16)=-17*4/16=-4.25
for 75 z=(75-62)/16/sqrt(16)=13*4/16=52/16=+3.25
probability z is between those two numbers is 0.9994.
While it is quite possible a woman may be less than or greater than 1 sd from the mean, it is highly unlikely a random sample of 16 of those women would be more than 1 sd from the mean.