/*! 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 97. Lactose intolerance Lactose into... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q 97. (page 331)

Lactose intolerance Lactose intolerance causes difficulty

in digesting dairy products that contain lactose (milk sugar). It is particularly common among people of African and Asian ancestry. In the United States

(ignoring other groups and people who consider themselves to belong to more than one race), 82%of the population is white, 14% is black, and 4% is

Asian. Moreover,15% of whites, 70% of blacks, and 90% of Asians are lactose intolerant.20

(a) What percent of the entire population is lactose intolerant?

(b) What percent of people who are lactose intolerant are Asian?

Short Answer

Expert verified

Part (a) The percentage of the entire population of being lactose intolerant is 25.70%

Part (b) P(Asian|lactose)=14.01%

Step by step solution

01

Part (a) Step 1. Given Information

P(White)=82%=0.82P(Black)=14%=0.14P(Asian)=4%=0.04
02

Part (a) Step 2. Concept used

Multiplication rule: P(A鈭�B鈭�C)=P(A)脳P(B)脳P(C)

03

Part (a) Step 3. Calculation

In response to the question:

P(lactose|white)=15%=0.15P(lactose|black)=70%=0.70P(lactose|Asian)=90%=0.90

Now, for each category, calculate the likelihood of being lactose intolerant:

P(lactose鈭�white)=P(lactose|white)脳P(white)=0.15脳0.82=0.2464P(lactose鈭�black)=P(lactose|black)脳P(black)=0.70脳0.14=0.098P(lactose|鈭�Asian)=P(lactose|Asian)脳P(Asian)=0.90脳0.04=0.0360

Fill in the blanks with the corresponding probabilities:

P(lactose)=0.1230+0.0980+0.360=0.2570鈬�P(lactose)=0.2570脳100=25.70%

As a result, 25.70 percent of the population suffers from lactose intolerance.

04

Part (b) Step 1. Concept

Conditional probability: P(A|B)=P(A鈭�B)/P(A)

05

Part (b) Step 2. Calculation

P(lactose)=0.2570

Conditional probability: P(A|B)=P(A鈭�B)/P(A)

As a result, we have:

P(Asian|lactose)=P(lactose鈭�Asian)P(Asian)=0.3600.2570鈮�0.1401=14.01%

As a result, Asians account for 14.01 percent of lactose-intolerant persons.

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

Taking the train According to New Jersey Transit, the 8:00 a.m. weekday train from Princeton to New York City has a 90% chance of arriving on time. To test this claim, an auditor chooses 6 weekdays at random during a month to ride this train. The train arrives late on 2 of those days. Does the auditor have convincing evidence that the company鈥檚 claim isn鈥檛 true? Design and carry out a simulation to answer this question. Follow the four-step process.

Shuffle a standard deck of cards, and turn over the top card. Put it back in the deck, shuffle again, and turn over the top card. Define events A: first card is a heart, and B: second card is a heart.

Brushing teeth, wasting water? A recent study reported that fewer than half of young adults turn off the water while brushing their teeth. Is the same true for teenagers? To find out, a group of statistics students asked an SRS of 60 students at their school if they usually brush with the water off. How many

students in the sample would need to say 鈥淣o鈥� to provide convincing evidence that fewer than half of the students at the school brush with the water off? The Fathom dot plot below shows the results of taking 200 SRSs of 60 students from a population in which the true proportion who brush with the

water off is 0.50.

(a) Suppose 27 students in the class鈥檚 sample say 鈥淣o.鈥� Explain why this result does not give convincing evidence that fewer than half of the school鈥檚 students brush their teeth with the water off.

(b) Suppose 18 students in the class鈥檚 sample say 鈥淣o.鈥� Explain why this result gives strong evidence that fewer than 50% of the school鈥檚 students brush

their teeth with the water off.

Rolling dice Suppose you roll two fair, six-sided dice鈥攐ne red and one green. Are the events 鈥渟um is 8鈥� and 鈥済reen die shows a 4鈥� independent? Justify

your answer.

Find the probability that the computer is a laptop. Show your work.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

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.