Q2. Cozco supermarket has determined that the number of cans of tomato soup sold
ID: 3320279 • Letter: Q
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Q2. Cozco supermarket has determined that the number of cans of tomato soup sold per day is approximately normally distributed with mean 60 and standard deviation 10 and that these numbers don't depend on the day of the week. a) What is the distribution of the number of cans of tomato soup sold per week (7 days) and how would you find the probability that the number of cans of tomato soup sold in a week (7 days) is >500? c) Every day at the close of business, the manager counts the number of cans of tomato soup left in stock. If the number is less than some threshold number 6, she places an order for more cans of soup. It takes 5 days for the order to be delivered and there can only be one outstanding order at a time. The manager wants to keep the inventory level as low as possible, but does not want to run out of product. She sets a goal that the probability of running out of stock (while waiting for an order to be delivered) should be no greater than 2%, what should be to achieve this goal? And how many cans of soup should be ordered?Explanation / Answer
a. The number of cans daily is nomally distributed with a mean of 60 and std. deviation of 10. So the distribution of the number of cans sold per week is normally distributed is also normally distributed with a mean of 7*60 = 420 and std. dev of 7*10 = 70
Now z = x-u/sigma =( 500 - 420/70) = 8/7=1.14
So on the standard normal curve, we should find the area under the curve to the right of x=1.14 in order to ascertain the probability that number of cans sold in a week >500.
(b) Since the sales on a daily basis is normally distributed 95% ofthe time th cans slod daily will be better 60 +- (2*std,Dev) = 60 +- 20 = From 40 to 80 cans and approx all sales done will be between 30 and 90 cans. So in oreder not to run out of the product and also to keep inventory levels as low as possible considering that it takes 5 days for one order to come then the minimum amount ordered shoulf be 90*7 = 630 cans at the start of the week
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