Chapter 5: Q. 5.3 (page 320)

A distribution is given as $X ~ U (0, 20)$ . What is $P (2 < x < 18)$ ? Find the $90^{th}$ percentile.

Short Answer

Expert verified

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

The value of the $90^{t h}$ percentile is $18$ .

Step by step solution

Given Information

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

We need to find what is $P (2 < x < 18)$ and $90^{t h}$ percentile.

Calculate the probability density function

Here, $X$ remains 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

$f (x) = \frac{1}{b - a}$

$= \frac{1}{20 - 0}$

$= \frac{1}{20}$

Calculate the value of P(2<x<18)

Let's find the required probability,

$P (2 < x < 18) = base \times height$

$= (18 - 2) \times (\frac{1}{20})$

$= 16 \times \frac{1}{20}$

$= 0.8$

Calculate the 90th percentile

Let's calculate the $90^{t h}$ percentile for $0 < x < 20$ as below

$P (x < k) = base \times height$

$0.90 = (k - 0) (\frac{1}{20})$

$or k - 0 = 0.90 \times 20$

$k = 18$

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A distribution is given as $X ~ U (0, 20)$ . What is $P (2 < x < 18)$ ? Find the $90^{th}$ percentile.

Short Answer

Step by step solution

Given Information

Calculate the probability density function

Calculate the value of P(2<x<18)

Calculate the 90th percentile

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

Short Answer

Step by step solution

Given Information

Calculate the probability density function

Calculate the value of P(2<x<18)

Calculate the 90th percentile

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Logic and Functions

Pure Maths

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

A distribution is given as $X ~ U (0, 20)$ . What is $P (2 < x < 18)$ ? Find the $90^{th}$ percentile.