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 lb.

A. What is the probability that a ball will be rejected? Round your answer to two significant digits.

B. 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.

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

D. What is the probability that three or more defective bowing balls are found in the first 25 examined? Do not do the calculation, but do write out the mathematical expression you would use to answer the question.