1.Your company purchases an expensive component from a supplier.You know that the population of the components is normally distributed with a mean ( ) of 60 months and a standard deviation ()of 2 months.Using this information determine:

a.the probability of a component lasting longer than 68 months.

b.the probability of a component lasting less than 63 months.

c.the probability that a components will last between 58 and 65 months.

2.Using the information in the problem above, what is the probability that a sample average () from a sample of 25 components will be between 58.5 and 59.6 months?

3.The revenues of gasoline stations are normally distributed with a population mean () of $2,200 per day and a population standard deviation () of $100.If you take a sample of 25 stations, what is the probability that the sample mean () will be:

a) More than $2,256.

b) Less than $2,194.

c) Between$2,160 and $2,190.

d) Less than $2,160 or more than $2,240.

4.An manufacturer of small electronic appliances knows that her products have a normally distributed lifespan with a mean of 20 months and a population standard deviation of 10 months.The manufacturer wants to establish a warranty for defective products.However, she wants to have to replace no more than 2.5% of the products that is, she wants the probability that a product fails within X months to be 0.025 or less.How many months should the warranty period (X) be?