At a recent state swim meet, all 8 and 9 year olds swam the 50 m. backstroke race. The mean completion time for girls was 80 seconds with a standard deviation of 10. The mean completion time for boys was 85 seconds with a standard deviation of 6. Distributions for both boys and girls are normal.
A. If 5 female competitors are randomly selected from the list of all participants, what is the expected value of the time it took all five of them, cumulatively, to complete their heats?
B. What is the probability that one female competitor chosen at random swam her heat faster than 93 seconds?
C. What is the probability that one male competitor chosen at random swam his heat slower than 93 seconds?
D. One characteristic of the normal distribution is that 95% of cases fall within two standard deviations of the mean. Given this, estimate the proportion of female swimmers who swam faster than 60 seconds
The solution to this problem is given by
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