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Are 20% of M&M Candies Orange? Mars, Inc. claims that 20%

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola ISBN: 9780321836960 18

Solution for problem 11BSC Chapter 5.4

Elementary Statistics | 12th Edition

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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Elementary Statistics | 12th Edition

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Problem 11BSC

Are 20% of M&M Candies Orange? Mars, Inc. claims that 20% of its M&M plain candies are orange, and a sample of 100 such candies is randomly selected.

a. Find the mean and standard deviation for the number of orange candies in such groups of 100.

b. Data Set 20 in Appendix В consists of a random sample of 100 M&Ms, including 25 that are orange. Is this result unusually high? Does it seem that the claimed rate of 20% is wrong?

Step-by-Step Solution:

Answer:

Step 1:   

            Given that, Mars, Inc. claims that 20% of its M&M plain candies are orange, and a sample of 100 such candies is randomly selected.

  Here, n = 100,p = 20% = 0.2, q = 1- p = 1- 0.2 = 0.8.

       a). The mean and standard deviation for the number of orange candies in such groups of 100.

              For binomial distribution the mean and variance is given by the following formula.

                 Here ‘x’ follows binomial distribution with sample size “n” and proportion “p”.      

                        i.e,   X

Probability mass function of binomial distribution is given by

       P(x) = , x = 0,1,2,...,n.

               Mean μ = np = 1000.2 = 20.

             Variance  = npq = 100(0.2)(0.8) = 16.

           And standard deviation =  =  =

 

Step 2 of 2

Chapter 5.4, Problem 11BSC is Solved
Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

The answer to “Are 20% of M&M Candies Orange? Mars, Inc. claims that 20% of its M&M plain candies are orange, and a sample of 100 such candies is randomly selected.a. Find the mean and standard deviation for the number of orange candies in such groups of 100.________________b. Data Set 20 in Appendix ? consists of a random sample of 100 M&Ms, including 25 that are orange. Is this result unusually high? Does it seem that the claimed rate of 20% is wrong?” is broken down into a number of easy to follow steps, and 80 words. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12. This full solution covers the following key subjects: candies, orange, such, sample, mean. This expansive textbook survival guide covers 121 chapters, and 3629 solutions. Since the solution to 11BSC from 5.4 chapter was answered, more than 822 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 11BSC from chapter: 5.4 was answered by , our top Statistics solution expert on 03/15/17, 10:30PM.

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