/*! 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} Problem 53 Lactose intolerance. Lactose int... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Lactose intolerance. Lactose intolerance causes difficulty 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. 22 (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
(a) 25.7% (b) 14% of lactose intolerant people are Asian.

Step by step solution

01

Calculate Lactose Intolerant Whites

First, we calculate the percentage of the total population that is white and lactose intolerant. We know that \(82\%\) of the population is white and \(15\%\) of them are lactose intolerant. So, the percentage of whites in the total population who are lactose intolerant is \(82\% \times 15\% = 0.82 \times 0.15 = 0.123 = 12.3\%\).
02

Calculate Lactose Intolerant Blacks

Next, we calculate the percentage of the total population that is black and lactose intolerant. \(14\%\) of the population is black and \(70\%\) of them are lactose intolerant. So, the percentage of blacks in the total population who are lactose intolerant is \(14\% \times 70\% = 0.14 \times 0.70 = 0.098 = 9.8\%\).
03

Calculate Lactose Intolerant Asians

Now, we calculate the percentage of the total population that is Asian and lactose intolerant. \(4\%\) of the population is Asian and \(90\%\) of them are lactose intolerant. Therefore, the percentage of Asians in the total population who are lactose intolerant is \(4\% \times 90\% = 0.04 \times 0.90 = 0.036 = 3.6\%\).
04

Calculate Total Lactose Intolerant Population

Sum the percentages of whites, blacks, and Asians who are lactose intolerant to find the total percent of the population that is lactose intolerant. \(12.3\% + 9.8\% + 3.6\% = 25.7\%\).
05

Calculate Percent of Lactose Intolerant Who Are Asian

To find the percent of lactose intolerant people who are Asian, divide the percentage of lactose intolerant Asians by the total percentage of lactose intolerant population and multiply by 100. This gives us \( \frac{3.6\%}{25.7\%} \times 100 = \frac{3.6}{25.7} \times 100 \approx 14\%\).

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 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Population Distribution
When we discuss population distribution, we are referring to the way different groups are spread out in a larger population. It is an important concept in statistics because it helps us understand broader socio-ethnic compositions and their potential implications. In our example, the population of the United States is broken down into three main racial groups for simplicity: White, Black, and Asian. These groups make up 82%, 14%, and 4% of the population, respectively.

Understanding this distribution helps in analyzing various social trends, including health issues like lactose intolerance. By knowing what proportion of the population each group represents, we can better understand the overall incidence of specific traits or health conditions across the entire population. In simpler terms, population distribution helps us frame our understanding of societal compositions and their characteristics.
Percentage Calculations
Percentage calculations are a fundamental aspect of turning raw data into meaningful insights. Percentages allow comparisons between disparate quantities, granting a more accessible means to interpret statistics.

For instance, to determine the percentage of the entire population that is lactose intolerant, we perform a series of percentage calculations. We calculate the portion of each racial group that is lactose intolerant and then combine these to find the overall rate.

In our example, we multiply the percentage of each racial group in the population by the percentage of people in that group who are lactose intolerant. This helps us find how many people from each group are affected. After finding these numbers, we add them up to discover that 25.7% of the whole population is lactose intolerant. This step-by-step approach makes it easier to synthesize complex data into understandable information.
Racial Demographics
Racial demographics influence many areas including public health, economics, and social policy. In examining lactose intolerance, understanding the racial demographics provides key insights.

Racial demographics in our example focus on White, Black, and Asian populations in the United States, each exhibiting different rates of lactose intolerance. Whites have a 15% incidence, Blacks 70%, and Asians 90%.
  • This variation can be attributed to genetic, environmental, and historical dietary practices within these groups.
  • Understanding these demographics and their associations with health conditions can help in planning public health initiatives.

By grasping the significance of racial demographics, researchers and policymakers can better address public health concerns and target educational resources to the populations most affected by certain conditions.
Data Analysis in Statistics
Data analysis in statistics is the process of inspecting, cleansing, and modeling data to discover useful information. It helps us answer questions and make informed conclusions. In the context of this exercise, data analysis allows us to determine the overall percentage of the lactose intolerant population and find the proportions of affected racial groups.

Through statistical analysis, we can break down complex questions into manageable parts:
  • By first calculating each group's lactose intolerant percentage,
  • And then summing these to find the total lactose intolerant population,
  • Finally, analyzing how these percentages translate to racial distribution within the affected population.

This methodical approach simplifies the understanding of large datasets and allows us to draw clear, actionable conclusions from seemingly overwhelming information. Thus, data analysis in statistics acts as a bridge between raw numerical data and practical insights for application in real-world settings.

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

Common Names. The U.S. Census Bureau says that the 10 most common names in the United States are (in order) Smith, Johnson, Williams, Brown, Jones, Miller, Davis, Garcia, Rodriguez, and Wilson. These names account for \(9.6 \%\) of all U.S. residents. Out of curiosity, you look at the authors of the texthooks for your current courses. There are nine authors in all. Would you be surprised if none of the names of these authors were among the 10 most common? (Assume that authors' names are independent and follow the same probability distribution as the names of all residents.)

At the Gym. Suppose that \(8 \%\) of adults belong to health clubs, and \(45 \%\) of these health club members go to the club at least twice a week. What percent of all adults go to a health club at least twice a week? Write the information given in terms of probabilities and use the general multiplication rule.

(Optional topic) Should the government help the poor? In the 2014 General Social Survey, \(32 \%\) of those sampled thought of themselves as Democrats, \(45 \%\) as Independents, \(21 \%\) as Republicans, and \(2 \%\) as Other. \({ }^{23}\) When asked, " Should the government in Washington do everything possible to improve the standard of living of all poor Americans?"" \(23 \%\) of the Democrats, \(18 \%\) of the Independents, \(4 \%\) of the Republicans, and \(15 \%\) of Others agreed. Given that a person agrees that the government in Washington should do everything possible to improve the standard of living of all poor Americans, use Bayes' rule to find the probability the person thinks of him- or herself as a Democrat.

Older College Students. Government data show that \(8 \%\) of adults are fulltime college students and that \(25 \%\) of adults are aged 55 or older. Nonetheless, we can't conclude that because \((0.08)(0.25)=0.02\), about \(2 \%\) of adults are college students 55 or older. Why not?

A probability teaser. Suppose (as is roughly correct) that each child bom is equally likely to be a boy or a girl and that the sexes of successive children are independent. If we let \(\mathrm{BG}\) mean that the older child is a boy and the younger child is a girl, then each of the combinations \(\mathrm{BB}, \mathrm{BG}, \mathrm{GB}, \mathrm{GG}\) has probability \(0.25\). Ashley and Brianna each have two children. (a) You know that at least one of Ashley's children is a boy. What is the conditional probability that she has two boys? (b) You know that Brianna's older child is a boy. What is the conditional probability that she has two boys?

See all solutions

Recommended explanations on Math Textbooks

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.