Question

To be legal for certain types of prize competitions, bowling balls must be very close to 16 lb. The weights of bowling balls from a certain manufacturer are known to be normally distributed with a mean of 16 lb. and a standard deviation of .25 lb. A ball will be rejected if it weighs less than 15.68

A.) Describe how you would use a table of random digits (comprised of 0,1,2,3, 4, 5, 6, 7 , 8, and 9) to simulate how long it would take to identify three defective bowling balls

B.) Use the numbers below to perform the simulation you described in part B, this time for three defective bowling balls. Repeat your simulation three times, starting with the first digit of the first line and proceeding left to right, starting again at the extreme left of each successive line. What is the average waiting-time based on your three simulations ?

77014 21414 95729 01392 37814 22931 94998 56569 30213 03469 16334 43057 03297 61609 68462 26199 98324 41436 96050 95744 98563 56006 93060 29402 76577 39814 75704 26127 42577 17458 25883 51840 45515 18925 46458 61380 79369 01710 93720 73046 16434 57044 23969 78022 67976 23279 67173 44918 91684 94775

Answer 1

Here mean = 16 lb

standard deviation = 0.25 lb

P(x < 15.68) = NORMDIST(x < 15.68; 16 lb ; 0.25 lb)

Z = (15.68 - 16)/0.25 = -1.28

P(x < 15.68) = NORMSDIST(-1.28) = 0.1

so as we come to know that probability to find a ball less than 15.68 is 0.10

so now we will assign 0 to yes and rest digits to no, and find three 0, and count the number of chances.

(B) First three zero are found in 42 attempts

Second three zero are found in 16 attempts

Third three zero are found in 34 attempts

so average waiting time for 3 simulations = (42 + 16 + 34)/3 = 30.67