Score: 0 of 5 pts 7 of 1216 complete 6.4.6-T The overhead reach distances of adu

Question

Score: 0 of 5 pts 7 of 1216 complete 6.4.6-T The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 8.6 cm. a. Find the probability that an individual distance is greater than 208.40 cm. b. Find the probability that the mean for 25 randomly selected distances is greater than 192.80 cm c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 303 a. The probability is Round to four decimal places as needed.) Enter vour an 2 remaining

Explanation / Answer

Params of normal distribution is as follows:

Mean = 195
Stdev = 8.6

a. P(X>208) = P(Z>208-195 / 8.6) = P(Z>1.512) = .0653

b. n = 25
So, P(X>192.8) = P(Z> (192.8-195)/(8.6/sqrt(25)) = P(Z>-1.279) = 0.8997

c.The Central limit theorm states that if population distribution is normal, then sample size doesn't matter, the
distribution of samples is still going to be normal

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