Let X,, X, X3, X4 X5, and Xg denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then thesex;s have a multinomial distribution. Suppose it is claimed that the color proportions are p, = 0.25, P2 = 0.13, P3 = 0.15, P4 = 0.2, P5 = 0.12, and Pe = 0.15.%3DA USE SALT(a) If n = 12, what is the probability that there are exactly two M&Ms of each color? (Round your answer to four decimal places.)(b) For n = 25, what is the probability that there at most four orange candies? [Hint: Think of an orange candy as a success and any other color as afailure.] (Round your answer to three decimal places.)(c) In a sample of 25 M&Ms, what is the probability that the number of candies that are blue, green, or orange is at least 11? (Round your answer tothree decimal places.)

X1.... X6 Color wise probability given We have to answer for mentioned questions. It will be solved…

Answered: et X,, X2, X3, X, X5, and X, denote the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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5. Inference.Consider the sample of students at the University of Reading in Table 3.Table 3: Hours spent studying per weekStudent ID. Hours spent studyingID1. 1ID2. 2ID3. 3ID4. 5ID5. 4ID6. 5ID7. 7ID8. 7ID9. 12ID10 5ID11. 7ID12 7ID13 15ID14. 0ID15. 3ID16. 4ID17. 4ID18 . 0ID19. 5ID20. 7ID21. 7ID22 . 13ID23. 7ID24. 9 a) Consider the possibility of using this sample to make…
C. A population consists of five numbers 1, 2, 3, 4, and 5. Consider samples of size 3 that can be drawn from this population. a. List all the possible samples and the corresponding mean SAMPLE MEAN 1 2 4 5 6 7 8 9 10 b. Construct the sampling distribution of the sample means find the mean Sampling Distribution of Sample Means Sample Mean (X) Probability P(X) Frequency X• P(X) 1 2 3 4 Hx = EX • P(X) = 6. So, the mean of the sampling distribution of the sample means is 7 9 10 c. Find the variance of the sampling distribution of the sample means P(X) X-u (X -µ)² P(X) • (X - 4)? 1 2 3 (o?2) = EP(X) • (X – )° %3D 6. 8 So, the variance of the 9. sampling distribution is 10
Cloud seeding has been studied for many decades as a weather modification procedure. The rainfall in acre-feet from 20 clouds that were selected at random and seeded with silver nitrate follows: 18.0, 30.7, 19.8, 27.1, 22.3, 18.8, 31.8, 23.4, 21.2, 27.9, 31.9, 27.1, 25.0, 24.7, 26.9, 21.8, 29.2, 34.8, 26.7, and 31.6. There is a claim that mean rainfall from seeded clouds exceeds 25 acre-feet. The P-value for the test H0: µ = 25 versus H1: µ > 25 is closest to:
1. Consider a ferry that can carry both buses and cars across a waterway. Each trip costs the owner approximately $12. The fee for cars is $2 and the fee for buses is $7. Let X and Y denote the number of buses and cars, respectively, carried on a given trip. The joint distribution of X and Y is given by Y/X 1 2 0.01 0.03 0.01 1 0.03 0.07 0.08 Y 0.03 0.06 0.06 0.07 0.13 0.07 0.12 0.03 0.04 0.08 0.02 0.06 A. Find the probability that there is exactly two cars and exactly one bus during a trip? B. What is the probability that there is almost one car and at most one bus during a trip? C. What is the probability that there is exactly one car during a trip? Exactly one bus?
Suppose that a set of ten measurements is drawn randomly. The sample consists of the set {1,1,0,15,2,3,4,0,1,3}. By inspection it is evident that the measurement x=15 appears unusually large in comparison to the rest of the measurements. Calculate the z-score equivalent for the measurement x=15 and determine if it is an outlier.
(2). location of its restaurants with the accompanying table of percentages. A restaurant is to be chosen at random from the 800 to test market a new style of chicken. A fast-food restaurant chain with 800 outlets in the United States describes the geographic Region SE SW NE Under 10,000 Population of City 10,000 - 100,000 Over 100,000 NW 0% 5% 5% 5% 6% 15% 4% 3% 15% 20% 12% 10% (a). population of 100,000 or less? Given that the restaurant chosen is in the northeast, what is the probability that the city it is in has a (b). that it is located in the northwest? Given that the restaurant chosen is in a city with population of 10,000 or more, what is the probability 1
ch 11 end. 5 : The XYZ Corporation is interested in possible differences in days worked by salaried employees in three departments in the financial area. A survey of 23 randomly chosen employees reveals the data shown below. Because of the casual sampling methodology in this survey, the sample sizes are unequal. Research question: Are the mean annual attendance rates the same for employees in these three departments?
6. The assumption of independent is violated whenever: None of these are true. There is a correlation between datapoints within one sample. The samples have unequal sizes. The population distribution is uniform.
f. The p-value for this sample = i. Thus, the final conclusion is A. There is insufficient evidence to conclude that the distribution of die rolls is not uniform. B.There is insufficient evidence to conclude that the die rolls are dependent. C.There is sufficient evidence to conclude that the distribution of die rolls is not uniform. D. There is sufficient evidence to conclude that the die rolls are dependent.
Truffles are a great delicacy, sending thousands of mushroom hunters into the forest each fall to find them. A set of plots of equal size in an old-growth forest in Northern California was surveyed to count the number of truffles (Water et al. 1997). The resulting distribution is pre- sented in the following table. Are truffles ran- domly located around the forest? If not, are they clumped or dispersed? How can you tell? (The mean number of truffles per plot, calculated from these data, is 0.60.) Number of truffles per plot 0 1 2 3 > 3 Frequency 203 39 18 13 15
Suppose that 20% of the residents in a certain state suppor an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion to be within 0.04 of the true proportion (i.e., between 0.16 and 0.24)? (Hint: Use the sampling distribution of the sample proportion in this case.) A. O It is certain that the resulting sample proportion will be within 0.04 of the true proportion. B. There is roughly a 99.7% chance that the resulting sample proportion will be within 0.04 of the true proportion. C. There is roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion. D. O There is roughly a 68% chance that the resulting sample proportion will be within 0.04 of the true proportion.

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