Suppose the demand for a company’s product in week 1,2, & 3 are each normally distributed. The means are 50, 45, and 65. The standard deviations are 10,5, and 15. Assume these 3 demands are...

Suppose the demand for a company’s product in week 1,2, & 3 are each normally distributed. The means are 50, 45, and 65. The standard deviations are 10,5, and 15. Assume these 3 demands are probabilistically independent.

Suppose the company has 180 units in stock, and it will not be receiving any more shipments from its supplier for at least 3 weeks.

What is the probability that stock will run out during the 3 week period?

How many units should the company have in stock, so that it can be 98% certain of not running out during the 3 week period , assuming it will not receive any more shipments during this period?