Answer to Question #269868 in Statistics and Probability for ggggg

Question

Suppose that the diameters of golf balls manufactured by a certain company are normally

distributed with mean of 1.96 inches and standard deviation of 0.04 in. A golf ball will be

considered defective if its diameter is less than 1.90 in. or greater than 2.04 in. What is the

percentage of defective balls manufactured by the company?

Answer 1

Let x be the diameter of a random ball, than X ~ $N(1.96,0.04^2)$ = 1.96 + 0.04N(0, 1)

Lets find the probability of the defective ball as 1 minus probability of a normal

$P(normal)=P(1.9<X<2.04)=P(1.9<1.96+0.04N(0, 1)<2.04)=P(-1.5<N(0, 1)<2)=P(N(0,1)<2)-P(N(0,1)<-1.5)=0.97725-0.06681=0.27333=0.91044\implies P(defective)=1-0.91044=0.08956$

So, the percentage of the defective balls is 100% * 0.08956 = 8.96%