Question

The length of time, in minutes, that a customer queues in a Bank is a random variable X with probability density function ?(?) = 1 486 (81 − ? 2 ), 0 ≤ ? ≤ 9 a. Find the probability that a customer will queue for longer than three minutes. (2 pts.) ?(? > 3) = 1 486 ∫ (81 − ? 2 )?? 9 3 = 1 486 (81? − ? 3 3 )| 3 9 = 1 486 ((81(9) − 9 3 3 ) − (81(3) − 3 3 3 )) = 252 486 = 14 27 = 0.5185 b. A customer has been queueing for three minutes, find the probability that this customer will be queueing for at least seven minutes.

Answer 1

a)

P(X > 3)

=

b)

P(X >= 7 |X > 3) = P(X >= 7 )/P(X > 3)

Now P(X > 3) = 14/27

P(X > = 7) =

hence required probability

= (50/729)/(14/27)

= 0.1322751

Please rate