Question

The frequency in which a restaurant receives​ on-line delivery orders follows an exponential distribution with a mean of 10.36 minutes between orders. Using this​ information, complete parts ​(a) through ​(f) for this question.

a) The probability that the restaurant will receive their next​ on-line delivery order in less than 5.1 minutes is

​(Round to four decimal places as​ needed.)

​b) The probability that the restaurant will wait between 9 and 11.4 minutes after getting a new​ on-line delivery order is

​(Round to four decimal places as​ needed.)

​c) The probability that the restaurant will wait more than 30.5 minutes before getting a new​ on-line delivery order is

​(Round to four decimal places as​ needed.)

​d) The probability that the restaurant will wait exactly 30.5 minutes before getting a new ​on-line delivery order is

​(Round to four decimal places as​ needed.)

​e) The amount of time such that 93% of the wait times between​ on-line delivery orders is less than this amount of time is ? minutes.

​(Round to two decimal places as​ needed.)

​f) The mean is this exponential distribution is ? minutes between​ on-line delivery orders with a standard deviation of ? minutes.

​(Round to two decimal places as​ needed.)

Answer 1

here for exponential distribution parameter β = 10.36

a()

P(X<5.1)=1-exp(-5.1/10.36)=

0.3888

b)

P(9<X<11.4)=(1-exp(-11.4/10.36)-(1-exp(-9/10.36))=

0.0867

c)

P(X>30.5)=1-P(X<30.5)=1-(1-exp(-30.5/10.36))=

0.0527

d)

The probability that the restaurant will wait exactly 30.5 minutes before getting a new ​on-line delivery order is =0.0000

e)

93th percentile =-10.36*ln(1-93/100)=

27.55 minutes

f)

The mean is this exponential distribution is 10.36 minutes between​ on-line delivery orders with a standard deviation of 10.36 minutes