Maria and Ralph are peeling apples The time it takes Maria t

Maria and Ralph are peeling apples. The time it takes Maria to peel an apple is approximately normally distributed with mean 12 seconds and standard deviation 2 seconds. The time it takes Ralph to peel an apple is approximately normally distributed with mean 11 seconds and standard deviation 2.5 seconds. 1. Find the probability that (starting together) Maria finishes her next apple before Ralph. 2. If the first person done always waits for the second person to finish (so that they always start together), Ralph will finish first ______ percent of the time.

Solution

1)

First you have to find the mean and sd of (maria - Ralph)

mean = 12-11 = 1
sd = sqrt (2^2 +2.5^2) - This is not a mistake you add not subtract. = 3.2

now its a normal curve problem N(1, 3.2) and you want the probability of m-r < 0 = .3773

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2)

Ralph will finish first (1-0.3773) * 100 = 62.27% of the times.