1) Mean amount purchased by customer at departmental Store is $23.50 with standard deviation of $5.00. Suppose distribution of amounts purchased follows normal distribution.  For sample of 50 customers, answer the problems given below.

a) Determine probability that sample mean is at least $25.00?

b) Determine probability that sample mean is more than $22.50 but less than $25.00?

c) In what limits would 90 percent of sample means occur?

2) Truck Lines service uses the ABC Super Duty F-750 exclusively. Management made study of the maintenance costs and found the number of miles travelled during year followed the normal distribution. Mean of the distribution was 60,000 miles and standard deviation 2,000 miles.

a) Determine the percent of ABC Super Duty F-750s logged 65,200 miles or more?

b) Determine the percent of trucks logged more than 57,060 but less than 58,280 miles?

c) Determine the percent of Fords travelled 62,000 miles or less during the year?

d) Is it logical to conclude that any of the trucks were driven more than 70,000 miles? Describe.