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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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