/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 5.28 Twelve percent of the population... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 5.28 (page 176)

Twelve percent of the population is left handed. Approximate the probability that there are at least 20 lefthanders in a school of 200 students. State your assumptions.

Short Answer

Expert verified

The probability that there are at least20lefthanders in a school of 200 is0.8365.

Step by step solution

01

Step 1. Given Information.

Twelve percent of the population is left handed.

So, P (left handed)=0.12

02

Step 2. Assumption

Assuming that except12%of the population all others are right handed.

03

Step 3. Approximate binomial distribution with normal distribution. 

P (left handed) =0.12

渭=200脳0.12=24

蟽=np(1-p)

Where, n=200and p=0.12

蟽=(200脳0.12)(1-0.12)蟽=24脳0.88蟽=21.12蟽鈮�4.60

P(X鈮�19.5)=PZ鈮�19.5-244.60=PZ鈮�-0.98=1-1-蠁0.98=0.8365

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

With 桅(x)being the probability that a normal random variable with mean 0and variance 1is less than x, which of the following are true:

(a)桅(-x)=桅(x)

(b)桅(x)+桅(-x)=1

(c)桅(-x)=1/桅(x)

The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by

f(x)=10x2x>100x鈮�10

(a)FindP{X>20}

localid="1646589462481" (b)What is the cumulative distribution function of localid="1646589521172" X?

localid="1646589534997" (c)) What is the probability that of6such types of devices, at least localid="1646589580632" 3will function for at least localid="1646589593287" 15hours? What assumptions are you making?

Let Xbe a uniform (0,1)random variable. Compute role="math" localid="1646717640777" EXnby using Proposition 2.1, and then check the result by using the definition of expectation.

Let Ube a uniform (0,1)random variable, and let a<bbe constants.

(a) Show that ifb>0, then bUis uniformly distributed on (0,b), and if b<0, then bUis uniformly distributed on (b,0).

(b) Show that a+Uis uniformly distributed on (a,1+a).

(c) What function of Uis uniformly distributed on (a,b)?

(d) Show that min(U,1-U)is a uniform (0,1/2)random variable.

(e) Show that max(U,1-U)is a uniform (1/2,1)random variable.

(a)A fire station is to be located along a road of lengthA,A<鈭�. If fires occur at points uniformly chosen on(0,A), where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to

minimize EX-a

whenXis uniformly distributed over (0,A)

(b)Now suppose that the road is of infinite length鈥� stretching from point0 outward to鈭�. If the distance of fire from the point 0is exponentially distributed with rate位, where should the fire station now be located? That is, we want to minimizeEX-a, where Xis now exponential with rate位.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.