Question

Suppose there is a rope company that produces rope by the bundle. The length of a bundle (in meters) is a random variable X~N(50,0.2). Calculate the following probabilities.

A.) The length of the bundle is less than 50.19 m

B.) the length of the bundle is greater than 50.16 m

C.) The length of the coil is between 50.16 m and 50.19 m

D.) Determine the positive number a such that p (50-a ≤ X ≤ 50 + a) = 0.9. Interpret the result.

Answer 1

Let X be the length of a bundle.

Given X~N(50,0.2)

a) Probability that the length of the bundle is less than 50.19 m is given by:

### by using Z table OR R command:

> pnorm(0.4249,0,1)
[1] 0.6645452

b) Probability that the length of the bundle is greater than 50.16 m is given by:

  

### By Z table Or Using R command:

> 1-pnorm(0.3578,0,1)
[1] 0.3602465

) Probability that the length of the coil is between 50.16 m and 50.19 m

d) Given p (50-a ≤ X ≤ 50 + a) = 0.9

That is

Therefore we have

a=0.7334