» Question 1: Traveling between two campuses of a university in a city via shutt

Question

» Question 1: Traveling between two campuses of a university in a city via shuttle bus takes, on average, 28 minutes with a standard deviation of 5 minutes. In a given week, a bus transported passengers 40 times. (a) What is the probability that the average transport time was more than 30 minutes? (b) What is the probability that the average transport time was more than 30 minutes given that it exceeds 20 minutes? (c) What is the probability that the total travelling time is greater than 1180 minutes?

Explanation / Answer

= 28 = 5 n = 40

(a) P(x > 30)

= P(z > ((30 - 28)/5 * 40))

= P(z > 2.5298)

= 0.0057.

(b) P(x > 20)

= P(z > ((20 - 28)/5 * 40))

= P(z > -10.1192)

= 1.

P(x >30 | x > 20)

= (1 - 0.0057) / 1

= 0.9943.

(c) 1180/40 = 29.5

P(x > 29.5)

= P(z > ((29.5 - 28)/5 * 40))

= P(z > 1.8974)

= 0.0289.

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