waiting times to receive food after placing an order at the local subway sandwich shop follow an exponential distribution with a mean of 60 seconds. calculate the probability a customer waits: a. less than 30 seconds. (round your answer to 4 decimal places.) b. more than 120 seconds. (round your answer to 4 decimal places.) c. between 45 and 75 seconds. (round your answer to 4 decimal places.)

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smecloudbird18 smecloudbird18 · Answer 1 · 2022-12-20T22:57:04+01:00

Waiting time follows an exponential distribution with mean

μ=60

μ=60 seconds. This implies λ=1μ=160λ= μ1= 601

Let X be the waiting time. for first we have to calculate the probability of customers who wait less than 30 secs.

a. X is less than 30 seconds, then we have to find ,

P(X<X1)=1−e−λX1⇒P(X<30)=1−e−λ×0

=1−e−160×30 =1−e−12=1−0.6065

=0.3935P(X<X 1)⇒

P(X<30)

=1−e −λX 1=

1−e −λ×30 1−e − 601×30 =

1−e − 21

=1−0.6065

=0.3935

b. X is more than 120 seconds, then we have to find less than 120 sec

b. X is more than 120 seconds

P(X>X1)=1−P(X<X1)=1−(1−e−λX1)⇒P(X>120)=1−(1−e−λ×120=e−60×120=e−2=0.135

P(X>X 1)⇒P(X>120)=1−P(X<X 1)=1−(1−e −λX 1)=1−(1−e −λ×120= − 601×120 =e −2=0.135

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