# Project #7909 - statistics

note: problems must be solved in excel

#1 Assume that the number of calories in a mcdonalds egg mcmuffin is a normally distributed random variable with a mean of 290 calories and a standard deviation of 14 calories.

a. what is the probability that a particular serving contains fewer than 300 calories?

b. more than 250 calories?

c. between 275 and 310 calories?

#2. the credit scores of 35 year olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 600 and a standard deviation of 100.

a. find the credit score that defines the upper 5 percent.

b. 75 percent of the customers will have a credit score higher than what value?

c. within what range woudl the middle 80 percent of credit scores lie?

#3 vail resorts pays part time seasonal employees at ski resorts on an hourly basis. at a certain mountain, the hourly rates have a normal distribution with standard deviation of \$3.00. if 20 percent of all part time seasonal employees make more than \$13.16 an hour, what is the average hourly pay rate at this mountain?

#4. the average cost of an IRS form 1040 tax filing at Thetis Tax Service is \$157.00. assuming a normal distribution, if 70 percent of the filings cost less than \$171.00, what is thr standard deviation?

#5 the time it takes to give a man a shampoo and haircut is normally distributed with mean 22 minutes and standard deviation 3 minutes. customers are scheduled every 30 minutes.

a. what is the probability that a male customer will take longer than the alloted time?

b. if three male customers are scheduled sequentially on the hald hour, what is the probability that all three will be finished within their alloted half hour time?

#6 the length of a time out during a televised professional football game is normally distributed with a mean of 84 seconds and a standard deviation of 10 seconds. if the network runs consecutive commercials totaling 90 seconds, what is the probability that play will resume before the commercials are over?

#7. the amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. the process has a standard deviation of 5ml. the mean is adjustable.

a. where should the mean be set to ensure 95% probability that a half-liter bottle will not be underfilled?

b. a 99 percent probability?

c. a 99.9 percent probability?

#8 the length of a brook trout is normally distributed. two brook trout are caught.

a. what is the probability that both exceed the mean?

b. neither exceeds the mean?

one if above the mean and one is below?

d. both are equal to the mean?

 Subject Mathematics Due By (Pacific Time) 06/17/2013 01:00 pm
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