Submit your calculation/answer for Part 1 and MATLABcode/result/answer for Part 2 below:

Servicing Customers A supermarket you work part-time at has oneexpress lane open from 5 to 6 PM on weekdays (Monday throughFriday). This time of the day is usually the busiest since peopletend to stop on their way home from work to buy groceries. Thenumber of items allowed in the express lane is limited to 10 sothat the average time to process an order is fairly constant atabout 1 minute. The manager of the supermarket notices that thereis frequently a long line of people waiting and hears customersgrumbling about the wait. To improve the situation he decides toopen additional express lanes during this time period. If he does,however, he will have to \"pull\" workers from other jobs around thestore to serve as cashiers. Hence, he is reluctant to open morelanes than necessary. Knowing that you are a college studentstudying probability, your manager asks you to help him decide howmany express lanes to open. His requirement is that there should beno more than one person waiting in line 95% of the time. With thetask at hand, you set out to study the problem first. You start bycounting the number of customer arrival in the express lane on aMonday from 5 to 6pm. There are a total of 81 arrivals. You repeatthe experiment on the following four days (Tuesday through Friday)and note the total arrivals of 68, 72, 61 and 66 customers,respectively.

Part 1: Analysis (2% of final grade) In order to solve theproblem, you decide to answer the following set of questions:

1)

2)Ans= 1.16

3) Ans = 67.71%

4) Ans= 96.53%

Part 2: Simulation (2% of final grade)

Before telling your manager your recommendation, you decide tosimulate the problem first to verify your solution:

1) You decide to approximate the customer arrival process asfollows. You treat each one-second interval as a Bernoulli trial.Assign it to be a one, if there is a customer arrives during thatinterval, zero if no customer arrives.

2) You count the number of customers arrives during a one-minuteinterval.

3) You count the total number of minutes out of a one-hourperiod that have two or fewer customers arrive. Does this numbergive your probability close to your calculation in Part 1 Prob3?

4) Now based on your answer to Part 1 Prob 4, assign thearrivals in Part 2 Prob 1 with equal probabilities to the number ofexpress lanes you recommend.

5) You count the number of customers arrives at each lane duringa one-minute interval.

6) You count the total number of minutes out of a one-hourperiod that all lanes have two or fewer customers arrive. Does thisnumber give you probability close to your calculation in Part 1Prob 4?

Done in MatLab please.