Question

(24 points)

1. 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.

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

Answer:

2. 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.

Answer:

3. 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	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:

4. What is the probability that three or more defective bowling 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.

Answer:

PLEASE DON'T COPY FROM EXISTING ANSWERS, THEY ARE NOT HELPFUL

Answer 1

a)

16 = 0.25 P(x < 15.68) = P( z < (15.68-16) / 0.25) = P(z < -1.28) = 0.1003 (from Normal probability table)