Question 1121626: For the questions below assume that females have pulse rates that are normally distributed with a mean of 74 beats per minute and a standard deviation of 12.5 beats per minute.
a. If 1 adult female is randomly selected, find the probability that her pulse is greater than 70 beats per minute.
b. If 25 adult female are randomly selected, find the probability that they have pulse rates with a mean greater than 70 beats per minute.
c. Why can the normal distribution be used in part (b) above, even though the sample size does not exceed 30?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x-mean)/sd
for a, z>(70-74)/12.5 or z>-0.32. That probability is 0.6255
b. z=(x-mean)/s/sqrt(n) or z>-4*sqrt(25)/12.5 or -1.6 That probability is 0.9452
c. If we can assume the population is normally distributed, then any sample size is appropriate. Thirty is not magic. If the population is significantly skewed, one may need a lot more than 30 or even a nonparametric test. If the population is normally distributed, 10 would be fine.
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