Columbia manufactures bowling balls with a mean weight of 14.4 pounds and a stan

Question

Columbia manufactures bowling balls with a mean weight of 14.4 pounds and a standard deviation of 2.2 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)

a) What is the probability that a randomly selected bowling ball is discarded due to being too heavy to use?

b) The lightest 7% 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

c) What is the probability that a randomly selected bowling ball will be discarded for being either too heavy or too light

Explanation / Answer

Here it is given that mean=14.4 and sd=2.2

a. It is given that bowling ball is discarded for being heavy over 16 pounds

So we need to find P(x>16)

As it is given this is normal distribution we will convert x to z

so P(z>16-14.4/2.2)=P(z>0.7273)=0.5-P(0<=z<=0.7273)=0.5-0.2665=0.2335

b. Here we need to find P(X<x)=0.07

Let us look for z, we get 0.5-P(0<=Z<=z)=0.07

So P(0<=Z<=z)=0.5-0.07=0.43        

Using z table we get P(0<=z<=-1.476)=0.43

So z=-1.476=x-mean/sd

so x=-1.476*2.2+14.4=11.1528

c. Now we need to find P(x>16 or x<11.1528)=P(z>0.7273 or z<-1.476)=0.3035

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