Resolve with excel

1. In determining automobile mileage ratings, it was found that the mpg in the city for a certain model is normally distributed, with a mean of 30 mpg and a standard deviation of 1.0 mpg. Suppose that the car manufacturer samples 5 cars from its assembly line and tests them for mileage ratings.
   1. What is the distribution of the mean mpg for the sample?
   2. What is the probability that the sample meanwillbe greater than 31 mpg?
   3. What is the probability that the sample mean be less than 29.5 mpg?
2. A popular soft drink is sold in 2-liter(2,000 milliliter) bottles.Because of variation in the filling process, bottles have a mean of 2,000 milliliterand a standarddeviation of 18, normally distributed.
   1. If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1,995 milliliters?
   2. What mean overfill or more will occuronly 10%of the time for the sample of 100 bottles?
3. A bank sampledits customers to determine the proportion ofcustomers who use their debit card at least once eachmonth. A sample of 50 customers found thatonly12 use their debit card monthly. Find 95% and 99%confidence intervals for the proportionof customers who use their debit card monthly.Use theappropriate formula and verify your result using theConfidence Intervals workbook.