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The table below shows the probability distribution of the discrete random variable X.          X 2 3 4 5 6 7 P(X=x) p 2p p 2p 3p p     Find the value of p from the table above.                                     Calculate the probability that at X is at least 5.                         Calculate the mean of the distribution.

The table below shows the probability distribution of the discrete random variable X.          X 2 3 4 5 6 7 P(X=x) p 2p p 2p 3p p     Find the value of p from the table above.                                     Calculate the probability that at X is at least 5.                         Calculate the mean of the distribution.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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  1. The table below shows the probability distribution of the discrete random variable X.

        

X

2

3

4

5

6

7

P(X=x)

p

2p

p

2p

3p

p

 

 

  1. Find the value of p from the table above.                                    
  2. Calculate the probability that at X is at least 5.                        
  3. Calculate the mean of the distribution.                                      

 

  1. A bottled water company has found in the past that 2% of their bottled water does not meet the company’s high standards. As such periodic samples are taken and tested for their quality. If from the last batch a sample of 12 bottles are taken and tested, determine the probability:

 

  1. i).Carefully defining the random variable of interest                                     
  2. ii). What is the probability distribution? State the values of the parameters   
  3. iii). Justifying the suitability of the probability distribution identified in part
  4. iv). Calculate the probability that at most 2 bottles do not meet the company's Standards                                 
  5. v). The expected number of bottles that do not meet the company’s standards.

 

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