SOLUTION: The ribbon-cutting ceremony for ACME�s new corporate headquarters is to be held tomorrow afternoon. Suppose the ribbon is tied between two posts set 8 feet apart. Let x be the di

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Question 1097652: The ribbon-cutting ceremony for ACME�s new corporate headquarters is
to be held tomorrow afternoon. Suppose the ribbon is tied between two
posts set 8 feet apart. Let x be the distance from the left post where the
CEO decides to make the cut. Assuming this is done at random, x
follows a uniform distribution on the interval from 0 to 8.
a. Sketch a graph of the density curve. Be sure to label appropriately.
b. Find the probability the CEO makes his cut somewhere between 2 feet and 5 feet from the left post.
I understand how to do part A but when it comes to B. I'm not sure where to start. I'm thinking this the probability density function but there is no mean or SD given. Thank you in advance for your help. I just need help in the right direction
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

The drawing done in part A is simply a rectangle that is 8 units wide and 1/8 of a unit tall. The width of 8 is because we go from 0 to 8, so 8-0 = 8. The height is 1/8 because want the total area of this rectangle to be 1

area of entire rectangle = (width)*(height) = 8*(1/8) = 1

Imagine having the rectangle's left edge start at x = 0. That would make the right-most edge at x = 8. In between these x values are x = 2 and x = 5. The area between x = 2 and x = 5 will represent the probability we want for part B

5-2 = 3 is the width of this sub-rectangle. The height is still 1/8

area of sub-rectangle = (new width)*(height) = (3)*(1/8) = 3/8 = 0.375

The answer as a fraction is 3/8 which is equivalent to the decimal form 0.375 (and that converts to 37.5%)