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Chapter 5: Q. 5.3 (page 320)

A distribution is given as X~U(0,20). What is P(2<x<18)? Find the90thpercentile.

Short Answer

Expert verified

The value of P(2<x<18)is 0.8.

The value of the 90thpercentile is18.

Step by step solution

01

Given Information 

Given in the question that, X~U(0,20)

We need to find what isP(2<x<18)and90thpercentile.

02

Calculate the probability density function 

Here, Xremains a random variable follows uniform distribution as X~U(a,b)

From the question X~U(0,20)

Where,

a=0

b=20

Hence, the probability density function or height of it will be

f(x)=1b鈭�a

=120鈭�0

=120

03

Calculate the value of P(2<x<18)

Let's find the required probability,

P(2<x<18)=base脳height

=(18鈭�2)脳120

=16脳120

=0.8

04

Calculate the 90th percentile

Let's calculate the 90thpercentile for 0<x<20as below

P(x<k)=base脳height

0.90=(k鈭�0)120

ork鈭�0=0.90脳20

k=18

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Most popular questions from this chapter

A subway train arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution. a. Define the random variable. X = _______ b. X ~ _______ c. Graph the probability distribution. d. f(x) = _______ e. 渭 = _______ f. 蟽 = _______ g. Find the probability that the commuter waits less than one minute. h. Find the probability that the commuter waits between three and four minutes. i. Sixty percent of commuters wait more than how long for the train? State this in a probability question, similarly to parts g and h, draw the picture, and find the probabilit

Use the following information to answer the next three exercises.

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

The probability of waiting more than seven minutes given a person has waited more than four minutes is?

a. 0.125

b. 0.25

c. 0.5

d. 0.75

Use the following information to answer the next three exercises.

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

79. What is the average waiting time (in minutes)?

a. zero

b. two

c. three

d. four

A continuous probability function is restricted to the portion between x = 0 and 7. What is P(x = 10)?

For a continuous probability distribution, 0鈮�x鈮�15. What is P(x>15)?
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