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Chapter 5: Question 80 (page 354)

Use the following information to answer the next three exercises.

The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.

80. Find the 30thpercentile for the waiting times (in minutes).

a. two

b.2.4

c.2.75

d. three

Short Answer

Expert verified

The 30th percentile for the waiting time is (b)2.4minutes

Step by step solution

01

Defining the Probability density function 

The Probability density function is given by :

f(x)=1(b-a),x∈(a,b)

02

Finding the30th probability

According to provided information, the random variable X for arrival of sky train is following uniform distribution such that:

X~U(0,8)fora=0andb=8

So, the Probability density function will be :

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

And, the 30thpercentile will be :

P(x<k)=base×height⇒0.30=(k-0)(18)⇒k=0.30×8=2.4

Hence, option (b) 2.4is the correct answer.

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