Question: Question 4

a) State three properties of a normal distribution.

b) A marketing manager of a leading firm believes that total sales for the firm next year can be modeled by using a normal distribution, with a mean of $2.5million and standard deviation of $300,000.

i. What is the probability that the firm’s sale will exceed $3 million?

ii. What is the probability that the firm’s sale will fall within $150,000 of the expected level of sales?

iii. In order to cover fixed costs, the firm’s sales must exceed the break-even level of $1.8 million. What is the probability that sales will exceed the break-even level?

iii. Determine the sales level that has only a 9% chance of being exceeded next year.