Question

The inside diameter of a randomly selected piston ring is a normally distributed random variable with mean 12 cm and standard deviation 0.04 cm. (a) What is the diameter that is exceeded by only 5% of the piston rings

Answer 1

`x=12.07`

Explanation:

From the question we are told that:

Mean
`\=x =12cm`

Standard deviation
`\sigma=0.04`

Significance level
`\alpha=5\%=0.05`

Therefore

Confidence level
`95\%=0.95`

From table
`P(z<1.645)=0.95`

Generally the equation for Z-score is mathematically given by

`z=(x-\mu)/(\sigma)`

`x=z\sigma+\mu`

`x=1.645*0.04+12`

`x=12.07`