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Chapter 6: Q 24. (page 372)

Where’s the bus? Sally takes the same bus to work every morning. Let X = the amount of

time (in minutes) that she has to wait for the bus on a randomly selected day. The

probability distribution of X can be modeled by a uniform density curve on the interval

from 0 minutes to8 minutes. Find the probability that Sally has to wait between 2 and 5

minutes for the bus.

Short Answer

Expert verified

The probability that Sally has to wait between 2 and 5 minutes for the bus is 37.5%.

Step by step solution

01

Step 1. Given information.

The distribution is modeled by a uniform distribution on the interval from 0 minutes to 8 minutes.

a=0,b=8

02

Step 2. To find the density curve.

The density curve of the uniform distribution is reciprocal of the difference of the boundaries

f(x)=1b-a=18-0f(x)=18f(x)=0.125

03

Step 3. To find the probability.

The probability, that the time is between 2 and 5 minutes, is then the area underneath the density curve between 2 and 5.

The area of a rectangle is the product of the width and the height.

P(2<X<5)=P(5-2)18=3×18=38=0.375=37.5%

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