Question

he production of pipes has a mean diameter of 3.25 inches and a standard deviation of .15 inches. The shape of the distribution is approximated by a normal distribution since approximately an equal number of parts are above or below average, and most parts are very close to the mean value. A part will be discarded is it has a diameter of greater than 3.5 inches or less than 3 inches. What proportion of parts are discarded from the production line

Answer 1

The probability that a randomly chosen part has diameter of 3.5 inches or more is 0.9525

Explanation:

`Mean = \mu = 3.25 inches`

Standard deviation =
`\sigma = 0.15 inches`

We are supposed to determine the probability that a randomly chosen part has diameter of 3.5 inches or more

`P(Z \geq 3.5)=1-P(z<(x-\mu)/(\sigma))\\P(Z \geq 3.5)=1-P(z<(3.25-3.5)/(0.15))\\P(Z \geq 3.5)=1-P(z<-1.67)`

Refer the z table for p value

`P(Z \geq 3.5)=1-0.0475\\P(Z \geq 3.5)=0.9525`

Hence the probability that a randomly chosen part has diameter of 3.5 inches or more is 0.9525