Question

(Round your answers to 4 decimal places.) owner hates to lose any business. What is the probabity that no cars w or more cars arriving during a one-hour period to use the diesel pump?

Answer 1

3.2 cars use the diesel pump every 2 hours.

a) Average number of cars arrival in one hour, $\lambda$ = 3.2/2 = 1.6 cars/hour

Probability that 3 cars will arrive in one hour period, P(X=3) =

  

є_λλ| є-1.61.63 0.1378 2 3!

b)Average number of cars arrival in half an hour, $\lambda$ = 3.2/4 = 0.8 cars/half hour

Probability that no cars will arrive in half hour period, P(X=0) =

  

or 0.4493

c) Average number of cars arrival in one hour, $\lambda$ = 3.2/2 = 1.6 cars/hour

Probability that 5 or more cars will arrive in half hour period, P(X>=5) = 1-P(X<5)

= 1 - [P(0)+P(1)+P(2)+P(3)+P(4)]

є_1.6 * 1.60 0! 10.9763 0.0237 e-1.6 * 1.61 1! e-1.6 * 1.62 2! €-1.6 * 1.63 3! є_1.6 * 1.64 4!

Either a rare event occurred or perhaps the long run average $\small \lambda$, has increased.