Question

A company making tires for bikes is concerned about the exact width of their cyclotrons tires. The company has a lower specification limit of 24.3 mm and an upper specification limit of 25.7 mm. The standard deviation is 0.15 mm and the mean is 25 mm.

What is the probability of a tire being too narrow (narrower than 24.3mm)?

What is the probability of a tire being too wide (wider than 25.7mm)?

Answer 1

We find exact probabilities using R:-

(i) P(Z<-4.66)

Using R

>pnorm(-4.66,0,1)

[1] 1.581047e-06

(ii) P(Z>4.66)

Using R

>pnorm(4.66,0,1,lower.tail=F)

[1] 1.581047e-06

Hence,the Probability of tire being too narrow (narrower than 24.3 mm) and too wide (wider than 25.7mm) is 1.581047e-06.