The diameter of a bolt produced by a manufacturer is a normal random variable wi

ID: 3176244 • Letter: T

Question

The diameter of a bolt produced by a manufacturer is a normal random variable with mean 1.20 inches and standard deviation of .005.

a. Fill in the blanks: about 95% of bolts have a diameter between _________ and ___________ inches.

b. For a randomly selected bolt, what is the probability that it is more than 1.215 inches in diameter?

c. The bolts are specified to be between 1.19 and 1.21 inches in diameter. What is the probability that a bolt does not meet the specifications?

d. What percent of bolts are more than 1.6 standard deviations from the mean?

Here mean=1.20 and sd=0.005

a. P(x1<x<x2)=0.95

using z table we get z==/-1.96

So x1=-1.96*0.005+1.20=1.1902

and x2=1.298

b. P(x>1.21)=P)(z>3)=0.0013

c. P(1.19<x<1.21)=P(-2<z<2)=0.9545

d. P(z>1.6*0.005)=P(z>0.008)