Question

Jackie goes into her McDonald's and chooses something to eat. On average, it takes her 4.0 minutes (or 240 seconds) to make a decision on what to buy.

a) What is the probability that it takes Jackie less than 2 minutes to make a decision?

b) If it has already been 107 seconds since Jackie entered the McDonald's, what is the probability it takes more than 240 seconds for Jackie to make a decision?

c) How much time would have passed for Jackie to be in the top 25% of the time it takes her to make a decision?

Answer 1

here for exponential distribution parameter β = 240 seconds

a)

probability that it takes Jackie less than 2 minutes(120 seconds) to make a decision :

P(X<120)=1-exp(-120/240)=

0.3935

b)

P(X>240|X>107) =P(X>(240-107=133)) =exp(-133/240)=0.5746

c)

for top 25% will be at 75th percentile:

pth percentile =-β*ln(1-p)

therefore 75th percentile =-240*ln(1-75/100)=

332.7106 seconds