Columbia manufactures bowling balls with a mean weight of 15.6 pounds and a stan
ID: 3178855 • Letter: C
Question
Columbia manufactures bowling balls with a mean weight of 15.6 pounds and a standard deviation of 0.3 pounds. A bowling ball is too heavy to use and is discarded if it weighs over 16 pounds. Assume that the weights of bowling balls manufactured by Columbia are normally distributed. (Round probabilities to four decimals) What is the probability that a randomly selected bowling ball is discarded due to being too heavy to use? the lightest 6% of the bowling balls made are discarded due to the possibility of defects. A bowling ball is discarded for being too light if it weighs under what specific weight? (Round weight to two decimals) pounds What is the probability that a randomly selected bowling ball will be discarded for being either too heavy or too light?Explanation / Answer
Mean ( u ) =15.6
Standard Deviation ( sd )=0.3
Normal Distribution = Z= X- u / sd ~ N(0,1)
a.
P(X > 16) = (16-15.6)/0.3
= 0.4/0.3 = 1.3333
= P ( Z >1.333) From Standard Normal Table
= 0.0912
b.
P ( Z < x ) = 0.06
Value of z to the cumulative probability of 0.06 from normal table is -1.555
P( x-u/s.d < x - 15.6/0.3 ) = 0.06
That is, ( x - 15.6/0.3 ) = -1.55
--> x = -1.55 * 0.3 + 15.6 = 15.1336
c.
either too heavy or too light = 0.0912 + 15.1336 = 15.2248