Question

Cars enter a car wash ata mean rate of 4 cars per half an hour. What is the probability that, in any hour, at least 3 cars will enter the car wash? Round your answer to four decimal places. Answer How to enter your answer Tables Keypad Keyboard Shortcuts Submit Answer LENG 9:28 AM 7/31/2020

Answer 1

Answer)

This question is a case of poisson distribution.

Mean rate for half an hour= 4 cars (Given)

According to poisson distribution-:

P(k events in an interval) = (e^-$\lambda$*$\lambda$^k )/k! where $\lambda$ is mean rate for that interval

Therefore, mean rate for an hour = $\lambda$ = 4*(mean rate for half an hour)= 8

Probability that atleast 3 cars will enter in an hour = P(x $\geq$ 3) = 1- P(x $\leq$ 2) = 1 - (P(0)+P(1)+P(2))

= 1 - e^-8(1+8+8²/2!) = 1 - e^-8(1+8+32) = 0.9863

Hence, Probability that atleast 3 cars will enter in an hour = 0.9863

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