You are the manager of a large warehouse/fulfillment center employing more than

Question

You are the manager of a large warehouse/fulfillment center employing more than a hundred workers. From historical information, you know that the number of orders that have to be fulfilled each day follows a Normal distribution with a mean of 6,000 orders per day, and a standard deviation of 800 orders. In the following problems you can either use the Normal probability table provided in CANVAS, the one on page 173 of the text, or use EXCEL to compute Normal probabilities. If you use a table, state which table and which row and column values you used. If you use EXCEL, write down the EXCEL formula you used in each case. Clear careful to SHOW YOUR CALCULATIONS. a). Let X be the number of orders on a randomly selected day. What is the probability that X exceeds 6400 orders? (B) What is the probability that the number of orders will fall between 5200 and 6800 orders? (c) (What is the probability that the number of orders will be less than 4,400? (d) Find the two numbers equally distant from the mean such that 90% of the time the number of orders falls between those two numbers (e) (1 Suppose that you know that it requires 5 workers to complete 400 orders in a day. How many workers to do you need to be 95% certain that you can complete all orders in a random day (round UP to make the answer a whole number of workers).

Explanation / Answer

excel formula are written along with calculation

a) probability that oder exceeds 6400 orders =P(X>6400) =1-P(X<6400) =1-normdist(6400,6000,800,true)

=1-0.6915 =0.3085

b)P(5200<X<6800)=normdist(6800,6000,800,true)-normdist(5200,6000,800,true)

=0.8413-0.1587 =0.6827

c)P(X<4400)=normdist(4400,6000,800,true) =0.02275

d)for middle 90% values fall between 5 and 95 th percentile

therefore corresponding values =norminv(0.05,6000,800) ; norminv(0.95,6000,800) =4684.12 ; 7315.88

e)for 95th percentile ; corresponding order quantilty =7315.88

therefore number of workers required =7315.88*5/4000=9.14 ~10 workers

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