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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

Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. If a bulb has already lasted 12 years, find the probability that it will last a total of over 19 years.

The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive.

  1. Find aand band describe what they represent.
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  5. What is the 65th percentile for the duration of games for a team for the 2011 season?

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