The amount of time required for a specialist to take an exam for professional ce

Question

The amount of time required for a specialist to take an exam for professional certification is between 1.5 and 4 hours. What is the probability that a randomly selected specialist will require more than two hours to take the exam? What is the probability that a randomly selected specialist will require less than three hours to take the exam? A city bus arrives at your bus stop every 8 minutes and follows a uniform distribution. The average wait time is_ The 30th percentile for wait times is_? The probability that a randomly selected person waits seven minutes or longer is_ The probability that a randomly selected person waits seven minutes or longer given that they have already waited two minutes is_?

Explanation / Answer

1) P(more than 2 hours) = (4-2)/(4-1.5) = 0.8

P(less than 3 hours) = (3-1.5)/(4-1.5) = 0.6

2) Average waiting time = (8+0)/2 = 4 minutes

Let A denote 30th percentile

(A - 0)/(8-0) = 0.3

A = 0.3x8 = 2.4 minutes

30th percentile for wait times is 2.4 minutes

P(7 minutes or longer) = (8-7)/8 = 0.125

P(7 minutes or longer | already waited two minutes) = (8-7)/(8-2)

= 1/6 = 0.1667

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