Question

A customer at the fabric store buys fabric that is 40 inches wide, i.e., 1.11 yards wide. The length is cut by the employee at the store. When she is asked to cut 1 yard of fabric, the actual length is Uniformly distributed between 0.87 and 1.05 yards. What is the probability that the entire piece of fabric has area 1 square yard or larger?

A = 1.11L

P(A > 1)

P(1.11L > 1)

P(L > 0.9009)

= (1.05 - 0.9009) / 0.18

= 0.8283

Where did 1.05 and 0.18 come from

Answer 1

Here' the answer to the question. please write back in case you've doubts.

To understand this lets understand the uniform distribution.

Uniform distribution has 2 parameters a, and b such that a and b are lower and upper bounds. Here in the diagram below a and b are these 2 points.

So, the probability of getting at least c ( c is a point between a and b) will be given by :

P(X> c) which in turn is = (a-c)/(b-a) ................Equation 1 ( check the red shaded are in the above image)

In our case, b is 1.05, a = 0.87 as given in the question. So, (b-a) = (1.05-.87) = 0.18. This is how you get the "0.18".

Also, 1.05 is the upper bound a. What you have done in your calculation is  (a-c) or (1.05 - .9009).

Hope that clears it!