ore:O of 2 pts 5.5 Assume that women\'s heights are normally distributed with a
ID: 3332022 • Letter: O
Question
ore:O of 2 pts 5.5 Assume that women's heights are normally distributed with a mean given by 1 of 4 (0 complete) -63.3 in, and a standard deviation given by #28 in (a) If 1 woman is randomly selected, find the probability that her height is less than 64 in. randomly selected, find the probability that they have a mean height less than 64 in. (a) The probability is approximately (Round to four decimal places as needed.) tent aLibra Enter your answer in the answer box and then click Cheok Answer Option part Tutor remaining e Tools To see what to study next, go to your Study Plan 16Explanation / Answer
a. Assume X denote the variable woemn's height. Use Z score formula to compute the required probability. P(X<64)=P[Z<(64-63.3)/2.8] [Z=(X-mu)/sigma, where, X is raw score, mu is population mean and sigma is population standard deviation].
=P(Z<0.25)=0.5987
b. According to Central Limit Theorem, the sampling distribution of sample means becomes normal in shape as sample size increases, with mean of sampling distribution becoming equal to population mean and and its' standard deviation equal to sigma/sqrt n. P(X<64)=P[Z<(64-63.3)/(2.8/sqrt n)]=P(Z<1.48)=0.9306
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