Probability question Im stumped

Question

 

A company has invested $100,000 in a plant which should meet all foreseeable demand for a patented product. The annual demand is normally distributed with a mean of of 20,000 units and a standard deviation of 4000 units. If the profit margin on each unit is $4 what is the probability that the company will recover its investment in one year?

Is this a bell curve and formula?

Answer 1

First need to figure out how many units will provide a profit of $100000 if each unit has a profit of $4: $100000/$4 = 25000. So will need to find the probability of selling at least 25000 units in a year if the annual sales has a mean of 20000 and a standard deviation of 4000.

If x is number of units want to find P(x > 25000).

z = (x - 20000)/4000 follows the standard normal distribution (mean 0 SD = 1)

Compute z for x = 25000: z = (25000 - 20000)/4000 = 1.25

so P(x > 25000) = P(z > 1.25) = 1 - P(z < 1.25) = 1 - 0.8944 = 0.1056.