6. To be legal for certain types of prize competitions, bowling balls must be ve
ID: 3160506 • Letter: 6
Question
6. 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
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
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.
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
Explanation / Answer
Let X be the random variable that the weights of bowling balls from a certain manufacturer.
X ~ Normal(mean = 16 lb, sd = 0.25 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.
That is here we have to find P(X < 15.68).
Now convert x = 15.68 into z-score.
z = (x - mean) / sd
z = (15.68 - 16) / 0.25 = -1.28
That is now we have to find P(Z < -1.28).
This probability we can find by using EXCEL.
syntax is,
=NORMSDIST(z)
where z is test statistic value.
P(Z < -1.28) = 0.1003
There is a slightly more than 10% chance that a bowling ball will be rejected.
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.
Pick one of those digits. Most people would pick zero. Follow along in the random digits table, counting digits, until you find your third zero.
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