A friend commutes by bus to and from work 6 days/week. Suppose that waiting time is uniformly distributed between 0 and 10 min, and that waiting times going and returning on various days are independent of each other. What is the approximate probability that total waiting time for an entire week is at most 75 min? To do that lets go step by step. (a) What is the mean and variance of waiting time? (b) What is the approximated probability distribution of the total waiting time? (c) What is the approximate probability that total waiting time for an entire week is at most 75 min?

MATLAB: An Introduction with Applications
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A friend commutes by bus to and from work 6 days/week. Suppose that waiting time
is uniformly distributed between 0 and 10 min, and that waiting times going and
returning on various days are independent of each other. What is the approximate
probability that total waiting time for an entire week is at most 75 min? To do that
lets go step by step.
(a) What is the mean and variance of waiting time?
(b) What is the approximated probability distribution of the total waiting time?
(c) What is the approximate probability that total waiting time for an entire week is
at most 75 min?
Assume a sequence of independent trials, each with probability p of success. Use the
Law of Large Numbers to show that the proportion of successes approaches p as the
number of trials becomes large.
Transcribed Image Text:A friend commutes by bus to and from work 6 days/week. Suppose that waiting time is uniformly distributed between 0 and 10 min, and that waiting times going and returning on various days are independent of each other. What is the approximate probability that total waiting time for an entire week is at most 75 min? To do that lets go step by step. (a) What is the mean and variance of waiting time? (b) What is the approximated probability distribution of the total waiting time? (c) What is the approximate probability that total waiting time for an entire week is at most 75 min? Assume a sequence of independent trials, each with probability p of success. Use the Law of Large Numbers to show that the proportion of successes approaches p as the number of trials becomes large.
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