Answer to Question #88352 in Statistics and Probability for Shivam Nishad

Question

Suppose the diameter x of a rod has normal distribution N (2, 0.16) . If the diameter x
satisfies 1.8 ≤ x ≤ 2.1 , then it is non-defective. Find the probability that the rod is non-defective

Answer 1

1) For the normal distribution N(2,016) the mean equals 2 and the standard deviation is 0.4.

If a rod has normal distribution N(2, 0.16), then P(1.8<X<2.1)=P((1.8-2)/0.4<Z<(2.1-2)/0.4)=P(-0.5<Z<0.25)=P(Z<0.25)-P(Z<-0.5)=

=P(Z<0.25)-1+P(Z<0.5)=0.5987-1+0.6915=0.2902.