Question

A manufacturing process makes rods that vary slightly in length but follow a normal distribution with mean length 25 cm and standard deviation 2.60. What is the probability of randomly selecting a rod that is shorter than 22 cm

Answer 1

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22) = 0.1251

Explanation:

Step(i):-

Given mean of the Population = 25cm

Given standard deviation of the Population = 2.60

Let 'x' be the random variable in normal distribution

Given x=22

`Z = (x-mean )/(S.D) = (22-25)/(2.60) = -1.15`

Step(ii):-

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22) = P( Z<-1.15)

= 1-P(Z>1.15)

= 1-( 0.5+A(1.15)

= 0.5 - A(1.15)

= 0.5 - 0.3749

= 0.1251

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22) = 0.1251