BUSINESS STATISTICS 271 FINAL EXAMINATION - JJ Chapter 6 Name______________________ 1. Date_______________ Compute the following probabilities or find the z values using the standard normal distribution table and draw a graph for each. a. b. c. P( -2.08 z ) P( -z1 z z1 ) = .8812 P( z 2.25) 2. In a recently conducted study, families reported using an average of 70 gallons of gasoline per month with a standard deviation of 9 gallons. If a family is chosen at random, what is the probability that it uses between 80 and 86 gallons of gasoline per month? Assume the data is normally distributed. 3. A stadium vendor serves draft beer in plastic cups. On average, the vendor places fourteen ounces of beer in each cup with a standard deviation of .35 ounces per cup. Assuming this is normally distributed, what is the probability that a customer will receive a cup containing less than 13 ounces of beer? Draw a graph to illustrate this problem. 4. The average time spent waiting in line at the drive-in window of a bank is seven minutes. What is the probability that a customer will spend between eight and twelve minutes waiting in line at the drive-in window? 5. Joe knows from experience that on average it takes thirty-five minutes to mow his yard. He really needs to mow the yard, but the big game kicks-off in forty-five minutes and he really wants to see that too. His DVR is not working and he really needs to mow that yard. What is the probability that he can finish mowing the yard before the start of the game? 6. The diameters of the holes in donuts produced by Krispy Kreme Donuts are normally distributed with a mean of 1.1 inches and a standard deviation of 0.10 inch. Of all donuts produced, 0.0075 are rejected because the donut holes are too small to fit over a rack on which the donuts are hung to cool. What is the diameter of the rack on which the donuts are hung? BUSINESS STATISTICS 271 FINAL PRACTICE EXAMINATION IV - Ch. 6 Name______________________ 1. Compute the following probabilities or find the z values using the standard normal distribution table and draw a graph for each. a. b. c. d. 2. Date_______________ P( -2.00 z ) (find the area or probability) P( z ?? ) = .025 (find the z number) P( -z1 0 z1 ) = .7814 (find the z numbers) P( - z 1.84) (find the area or probability) The mean time required to complete a statistics test is 60 minutes and completion times follow an exponential distribution. If the class period is 75 minutes and there are 50 students in the class, how many of them will not finish the test before the end of the class period? 3. The charge of a certain group of batteries is normally distributed with a mean value of 12.2 volts and a standard deviation of .5 volts. What proportion of the batteries should be expected to have a charge of more than 12 volts? Draw a graph (curve) to illustrate. 4. The average time a student spends standing in line to register for fall classes at a local college is eight minutes. If wait times are independent and constant, what is the probability the student will spend no more than ten minutes waiting in the line? 5. Magician Marco the Magnificent loves to pull rabbits out of his magic top hat, but he has to make sure the rabbits will fit into his hat first. He knows that the size of rabbits is normally distributed and that the average rabbit has a mean diameter of 8 inches with a standard deviation of 2 inches. Of all rabbits available for magic tricks, 2.5% cannot be used because they are too big to fit in his hat. In inches, what is the diameter of Marco's magic hat