# Answer in Statistics and Probability for NONKU #248827

Nite Time Inn has a toll-free telephone number so that customers can call at any time to make a reservation. A typical call takes about 4 minutes to complete, and the time required follows an exponential distribution. Find the probability (by hand and using MS Excel) that a call takes: 3 minutes or less.

exceed 5 minutes

a.

Under exponential distribution, parameter “lambda” tells the probability that some process will last a given amount of time or less. In this case, a typical call takes about 4 minutes to complete, so

“1divlambda=4”

“lambda=1div4 = 0.25”

The probability that a call takes 3 minutes or less is:

“P(timeseqslantless T) = 1-e^{-lambda*T}”

“P(times eqslantless3) = 1 – e^{-0.25*3}=1-e^{-0.75}”

In MS Excel, EXP function is used to determine the value of e-0.75. As per MS Excel, e-0.75 is 0.472.

“P(times eqslantless3) = 1 – 0.472 =0.528”

This means there is 52.8% probability that a call takes 3 minutes or less.

b.

The probability that a call exceed(takes longer than) 5 minutes is:

“P(timeeqslantless5)+P(timeeqslantgtr5)=1”

“P(time>5) = 1-P(timeeqslantless5)”

“P(time>5) = 1-(1-e^{-0.25*5} )”

“P(time>5) = 1-1+e^{-1.25}”

In MS Excel, EXP function is used to determine the value of e-1.25. As per MS Excel, e-1.25 is 0.287.

“P(time>5) =1-1+0.287 = 0.287”

So, it can say that there is 52.8% probability of a call exceeding 5 minutes.

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