
(a)
To make: a Venn diagram with information and consider options when labeling the diagram.
(a)

Answer to Problem 10.8AYK
The Venn diagram was constructed.
Explanation of Solution
Given:
An African study tested 543 children for the sickle-cell anemia trait and for malaria infection. Of those tested, 25% had sickle-cell, 34.6% had malaria and 6.6% had both sickle cell and malaria.
Calculation:
Based on this information a Venn diagram can be constructed. To do this, the probabilities of both malaria and not sickle-cell and sickle-cell and not malaria need to be calculated as follows:
To calculate the
From this, the probability that a child has neither sickle cell nor malaria can be calculated by taking 1 minus this above calculated value.
These values can now be used to complete the Venn diagram.
Conclusion:
Therefore, the Venn diagram was constructed.
(b)
To find: the probability that a given child has either malaria or the sickle-cell trait.
(b)

Answer to Problem 10.8AYK
The probability that a child has either malaria or sickle cell is 0.53.
Explanation of Solution
Calculation:
The probability that a given child has neither malaria nor sickle cell can be seen in the Venn diagram. In addition, to calculate the probability that a child has neither sickle cell nor malaria, first the probability a child has either sickle cell or malaria needs to be determined.
From this, the probability that a child has neither sickle cell nor malaria can be calculated by taking 1 minus this value.
The probability that a child has neither sickle cell nor malaria is 0.47.
Also, the probability that a child has either malaria or sickle cell can be determined using the given information. To do this, the probability that a child has sickle cell is added to the probability that a child has malaria. This value is then subtracted from the probability that a child has both.
Conclusion:
Therefore,the probability that a child has either malaria or sickle cell is 0.53.
(c)
To find: the probability that a given child has malaria, given that the child has the sickle-cell trait.
(c)

Answer to Problem 10.8AYK
The probability that a child has malaria given they do not have sickle cell is 0.373.
Explanation of Solution
Calculation:
The probability that a child has malaria given that a child has sickle cell is expressed as follows:
The probability that a child has malaria given they have sickle cell is 0.264.
The probability that a child has malaria given that they do not have sickle cell is expressed as follows:
First, the probability that a child does not have sickle cell needs to be determined by taking 1 minus the probability that a child has sickle cell (0.25).
Next, substitute the values into the formula given above.
Conclusion:
Therefore,the probability that a child has malaria given they do not have sickle cell is 0.373.
(d)
To describe: the
(d)

Answer to Problem 10.8AYK
Therefore, the probability of malaria and sickle cell using the multiplication rule gives a probability of 0.0865.As a result, these two events are not independent.
Explanation of Solution
Calculation:
To verify independence, the multiplication of the probabilities of malaria and sickle cell should be equal to the probability of malaria and sickle cell, which is 0.066.
Calculating the probability of malaria and sickle cell using the multiplication rule gives a probability of 0.0865. This is greater than and does not match the probability of both malaria and sickle cell of 0.066 as given in the example. As a result, these two events are not independent.
Conclusion:
Therefore, the probability of malaria and sickle cell using the multiplication rule gives a probability of 0.0865.As a result, these two events are not independent.
Want to see more full solutions like this?
Chapter 10 Solutions
EBK PRACTICE OF STATISTICS IN THE LIFE
- Client 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127arrow_forwardClient 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127 a) Determine the mean change in patient weight from before to after the diet (after – before). What is the 95% confidence interval of this mean difference?arrow_forwardIn order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forward
- If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…arrow_forwardProblem 1: The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is: Between the mean and $45 per hour? More than $45 per hour? Less than $32 per hour? Problem 2: The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds. What is the area between 415 pounds and the mean of 400 pounds? What is the area between the mean and 395 pounds? What is the probability of randomly selecting a value less than 395 pounds? Problem 3: In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution. What percent of New York State high school teachers earn between 70,000 and 75,000? What percent of New York State high school…arrow_forwardPls help asaparrow_forward
- Solve the following LP problem using the Extreme Point Theorem: Subject to: Maximize Z-6+4y 2+y≤8 2x + y ≤10 2,y20 Solve it using the graphical method. Guidelines for preparation for the teacher's questions: Understand the basics of Linear Programming (LP) 1. Know how to formulate an LP model. 2. Be able to identify decision variables, objective functions, and constraints. Be comfortable with graphical solutions 3. Know how to plot feasible regions and find extreme points. 4. Understand how constraints affect the solution space. Understand the Extreme Point Theorem 5. Know why solutions always occur at extreme points. 6. Be able to explain how optimization changes with different constraints. Think about real-world implications 7. Consider how removing or modifying constraints affects the solution. 8. Be prepared to explain why LP problems are used in business, economics, and operations research.arrow_forwardged the variance for group 1) Different groups of male stalk-eyed flies were raised on different diets: a high nutrient corn diet vs. a low nutrient cotton wool diet. Investigators wanted to see if diet quality influenced eye-stalk length. They obtained the following data: d Diet Sample Mean Eye-stalk Length Variance in Eye-stalk d size, n (mm) Length (mm²) Corn (group 1) 21 2.05 0.0558 Cotton (group 2) 24 1.54 0.0812 =205-1.54-05T a) Construct a 95% confidence interval for the difference in mean eye-stalk length between the two diets (e.g., use group 1 - group 2).arrow_forwardAn article in Business Week discussed the large spread between the federal funds rate and the average credit card rate. The table below is a frequency distribution of the credit card rate charged by the top 100 issuers. Credit Card Rates Credit Card Rate Frequency 18% -23% 19 17% -17.9% 16 16% -16.9% 31 15% -15.9% 26 14% -14.9% Copy Data 8 Step 1 of 2: Calculate the average credit card rate charged by the top 100 issuers based on the frequency distribution. Round your answer to two decimal places.arrow_forward
- Please could you check my answersarrow_forwardLet Y₁, Y2,, Yy be random variables from an Exponential distribution with unknown mean 0. Let Ô be the maximum likelihood estimates for 0. The probability density function of y; is given by P(Yi; 0) = 0, yi≥ 0. The maximum likelihood estimate is given as follows: Select one: = n Σ19 1 Σ19 n-1 Σ19: n² Σ1arrow_forwardPlease could you help me answer parts d and e. Thanksarrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman





