Question

A machine produces bolts with mean length 4 mm and a standard deviation of 0.3 mm. Bolts are measured and any which are shorter than 3.5 mm or longer than 4.4 mm are rejected. Calculate the proportion of bolts that are rejected. You are to assume the lengths are Normally distributed.

Answer 1

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 4

S.d = 0.3

P(3.5 < x < 4.4) = p(x<4.4) - p(x<3.5)

P(x<4.4)

Z = (4.4 - 4)/0.3 = 1.33

From z table, P(z<1.33) = 0.9082

P(x<3.5)

Z = (3.5 - 4)/0.3 = -1.67

From z table, P(z<-1.67) = 0.0475

P(3.5 < x < 4.4) = 0.9082 - 0.0475 = 0.8607

Now we need the.probability p(x>4.4) + p(x<3.5)

= 1 - ((p(3.5<x<4))

= 1 - 0.8607

= 0.1393 is the required answer