Maddie has two different routes that she can take to get to school. The first route is a longer ditace but has no traffic lights. The second route is a shorter distance, but has a lot of traffic lights. The amount of time it takes to get to school by the "longer distance" route follows a Normal distribution with mean 20 minutes and standard deviation q =1.5 minutes. The amount of time it takes to get to school by the "shorter distance" route follows a Normal distribution with mean = 17 minutes and standard deviation a = 6.5 minutes. Suppose we select independent random samples of 20 days for each route. Let X-Xs be the difference in the sample mean travel time for the two routes %3D (a) Calculate the probability that the sample mean time for the longer distance is shorter than the sample mean time for the shorter distance.
Maddie has two different routes that she can take to get to school. The first route is a longer ditace but has no traffic lights. The second route is a shorter distance, but has a lot of traffic lights. The amount of time it takes to get to school by the "longer distance" route follows a Normal distribution with mean 20 minutes and standard deviation q =1.5 minutes. The amount of time it takes to get to school by the "shorter distance" route follows a Normal distribution with mean = 17 minutes and standard deviation a = 6.5 minutes. Suppose we select independent random samples of 20 days for each route. Let X-Xs be the difference in the sample mean travel time for the two routes %3D (a) Calculate the probability that the sample mean time for the longer distance is shorter than the sample mean time for the shorter distance.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:Maddie has two different routes that she can take to get to school. The first route is a longer distance,
but has no traffic lights. The second route is a shorter distance, but has a lot of traffic lights. The
amount of time it takes to get to school by the "longer distance" route follows a Normal distribution
with mean 20 minutes and standard deviation o = 1.5 mirutes. The amount of time it takes to get
to school by the "shorter distance" route follows a Normal distribution with mean =17 minutes and
standard deviation a = 6.5 minutes. Suppose we select independent random samples of 20 days for
each route. Let XL-Xs be the đifference in the sample mean travel time for the two routes
%3D
%3D
(a) Calculate the probability that the sample mean time for the longer distance is shorter than
the sample mean time for the shorter distance.
(b) Should we be surprised if the sample mean time for the longer distance is shorter than the
sample mean time for the shorter distance?
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