
Concept explainers
a.
Find the
a.

Answer to Problem 60CE
The sample space is,
Explanation of Solution
The given information is that the M&Ms were blended in the ratio of 13% brown, 14% yellow, 13% red, 24% blue, 20% orange and 16% green. Also, the selected random sample of M&M blended in the large bag is 2.
Sample space:
The set of all possible outcomes of the random experiment is said to be sample space of and it is denoted by S.
Consider, B represents brown, Y represents yellow, R represents red, BL represents blue, O represent orange and G represents green.
The all possible outcomes of the random experiment of any two of brown, yellow, red, blue, orange and green M&Ms is as follows.
b.
Find the
b.

Answer to Problem 60CE
The probability that both are brown is 0.0169.
Explanation of Solution
Calculation:
From the given information, it can be observed that the probability of brown M&M is 0.13
The probability that both are brown is obtained as follows:
Thus, the probability that both are brown is 0.0169.
c.
Find the probability that both are blue.
c.

Answer to Problem 60CE
The probability that both are blue is 0.0576.
Explanation of Solution
Calculation:
From the given information, it can be observed that the probability of blue M&M is 0.24
The probability that both are blue is obtained as follows:
Thus, the probability that both are blue is 0.0576.
d.
Find the probability that both are green.
d.

Answer to Problem 60CE
The probability that both are green is 0.0256.
Explanation of Solution
Calculation:
From the given information, it can be observed that the probability of green M&M is 0.16
The probability that both are green is obtained as follows:
Thus, the probability that both are green is 0.0256.
e.
Find the probability of one brown and one green M&M.
e.

Answer to Problem 60CE
The probability of one brown and one green M&M is 0.0208.
Explanation of Solution
Calculation:
The probability of one brown and one green M&M is obtained as follows:
Thus, the probability of one brown and one green M&M is 0.0208.
f.
Take 100 samples of two M&Ms (with replacement). Record the frequencies of each outcome listed in (b) and (c) and how close the empirical results come to the people prediction.
f.

Explanation of Solution
Calculation:
Answers may vary. One of the possible answers is as follows:
All 100 samples of two M&Ms (with replacement) is,
The number of frequencies for both are brown is 7 and the number of frequencies for both are blue is 9 and a total number frequency is 100.
For (b) probability that both are brown:
The probability that both are brown is obtained as follows:
Thus, the probability that both are brown is 0.07.
For (c) probability that both are blue:
The probability that both are blue is obtained as follows:
Thus, the probability that both are blue is 0.09.
From part (b) and (c), the probability that both are brown is 0.0169 and the probability that both are blue is 0.0576.
From the results, it is observed that the empirical results are greater than the results of part (b) and (c). That is,
g.
Identify which definition of probability applies in the given situation.
g.

Answer to Problem 60CE
The definition of probability applies in the given situation is empirical.
Explanation of Solution
Classical Probability:
If each outcome in a sample space is equally likely to occur then it is said to be classical probability.
Empirical Probability:
The observations which are found from probability experiment is termed as empirical probability.
Subjective Probability:
If the probabilities result from intuition, educated guesses and estimates, then the probability is said to be subjective probability.
Here, the situation is most likely based on an experiment. That is, the number of each outcome is noted and the corresponding probabilities are obtained.
Thus, the definition of probability applied in the given situation is empirical.
Want to see more full solutions like this?
Chapter 5 Solutions
Applied Statistics in Business and Economics
- 1. A consumer group claims that the mean annual consumption of cheddar cheese by a person in the United States is at most 10.3 pounds. A random sample of 100 people in the United States has a mean annual cheddar cheese consumption of 9.9 pounds. Assume the population standard deviation is 2.1 pounds. At a = 0.05, can you reject the claim? (Adapted from U.S. Department of Agriculture) State the hypotheses: Calculate the test statistic: Calculate the P-value: Conclusion (reject or fail to reject Ho): 2. The CEO of a manufacturing facility claims that the mean workday of the company's assembly line employees is less than 8.5 hours. A random sample of 25 of the company's assembly line employees has a mean workday of 8.2 hours. Assume the population standard deviation is 0.5 hour and the population is normally distributed. At a = 0.01, test the CEO's claim. State the hypotheses: Calculate the test statistic: Calculate the P-value: Conclusion (reject or fail to reject Ho): Statisticsarrow_forward21. find the mean. and variance of the following: Ⓒ x(t) = Ut +V, and V indepriv. s.t U.VN NL0, 63). X(t) = t² + Ut +V, U and V incepires have N (0,8) Ut ①xt = e UNN (0162) ~ X+ = UCOSTE, UNNL0, 62) SU, Oct ⑤Xt= 7 where U. Vindp.rus +> ½ have NL, 62). ⑥Xn = ΣY, 41, 42, 43, ... Yn vandom sample K=1 Text with mean zen and variance 6arrow_forwardA psychology researcher conducted a Chi-Square Test of Independence to examine whether there is a relationship between college students’ year in school (Freshman, Sophomore, Junior, Senior) and their preferred coping strategy for academic stress (Problem-Focused, Emotion-Focused, Avoidance). The test yielded the following result: image.png Interpret the results of this analysis. In your response, clearly explain: Whether the result is statistically significant and why. What this means about the relationship between year in school and coping strategy. What the researcher should conclude based on these findings.arrow_forward
- A school counselor is conducting a research study to examine whether there is a relationship between the number of times teenagers report vaping per week and their academic performance, measured by GPA. The counselor collects data from a sample of high school students. Write the null and alternative hypotheses for this study. Clearly state your hypotheses in terms of the correlation between vaping frequency and academic performance. EditViewInsertFormatToolsTable 12pt Paragrapharrow_forwardA smallish urn contains 25 small plastic bunnies – 7 of which are pink and 18 of which are white. 10 bunnies are drawn from the urn at random with replacement, and X is the number of pink bunnies that are drawn. (a) P(X = 5) ≈ (b) P(X<6) ≈ The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a) The probability that the Grinch gets exactly 6 blue marbles is [ Select ] ["≈ 0.054", "≈ 0.043", "≈ 0.061"] . (b) The probability that the Grinch gets at least 7 blue marbles is [ Select ] ["≈ 0.922", "≈ 0.905", "≈ 0.893"] . (c) The probability that the Grinch gets between 8 and 12 blue marbles (inclusive) is [ Select ] ["≈ 0.801", "≈ 0.760", "≈ 0.786"] . The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a)…arrow_forwardSuppose an experiment was conducted to compare the mileage(km) per litre obtained by competing brands of petrol I,II,III. Three new Mazda, three new Toyota and three new Nissan cars were available for experimentation. During the experiment the cars would operate under same conditions in order to eliminate the effect of external variables on the distance travelled per litre on the assigned brand of petrol. The data is given as below: Brands of Petrol Mazda Toyota Nissan I 10.6 12.0 11.0 II 9.0 15.0 12.0 III 12.0 17.4 13.0 (a) Test at the 5% level of significance whether there are signi cant differences among the brands of fuels and also among the cars. [10] (b) Compute the standard error for comparing any two fuel brands means. Hence compare, at the 5% level of significance, each of fuel brands II, and III with the standard fuel brand I. [10]arrow_forward
- Analyze the residuals of a linear regression model and select the best response. yes, the residual plot does not show a curve no, the residual plot shows a curve yes, the residual plot shows a curve no, the residual plot does not show a curve I answered, "No, the residual plot shows a curve." (and this was incorrect). I am not sure why I keep getting these wrong when the answer seems obvious. Please help me understand what the yes and no references in the answer.arrow_forwarda. Find the value of A.b. Find pX(x) and py(y).c. Find pX|y(x|y) and py|X(y|x)d. Are x and y independent? Why or why not?arrow_forwardAnalyze the residuals of a linear regression model and select the best response.Criteria is simple evaluation of possible indications of an exponential model vs. linear model) no, the residual plot does not show a curve yes, the residual plot does not show a curve yes, the residual plot shows a curve no, the residual plot shows a curve I selected: yes, the residual plot shows a curve and it is INCORRECT. Can u help me understand why?arrow_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





