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#### marcadams267

##### New member

- Aug 26, 2019

- 8

1. Suppose that the service time for a student enlisting during enrollment is modeled as an

exponential RV with a mean time of 1 minute. If the school expects 500 students during

enrollment period, what is the probability that the registration committee will finish enlisting all

students within a day if a day constitutes a total of 8 working hours? Use the Central Limit

Theorem.

2. Suppose that you have a class at 8:45 am and you left your house at 8:00 am. To get to class, you

ride a train, ride a taxi and then walk. The train waiting time, train trip time, taxi waiting time, taxi trip time,

and walking time are all modeled as exponential random variables with a mean time of 10 mins,

and they are assumed to be independent of each other. What is the probability that you will not

be late for class?

My attempted solution:

1. Since mean time is 1 minute, and there are 480 mins in 8 hours, mean amount of students = 480

Variance = 1/λ^2, so standard deviation = 1/λ = mean = 480

Central limit theorem: Z = (S - mean)/standard_deviation --> (500-480)/480 = 0.0416666666

2. Since all the waiting times are identical, I add them up and get a mean time of 50 mins.

λ = 1/50 = 0.02

probability for an exponential random variable is λe^-(λt)

I then solve for the integral from 0 to 45 for 0.02e^-(0.02t) dt = 0.59344

Are my answers correct?