Px5 Px3 Px11 Explain why is Px11 greater than Px3 BA210 Tes

BA210, Test #2a, Autumn 2015, Discrete Random Variables, 100 points possible Instructions: Use the data on your test to solve each item. Write your answers in the blanks provided. Round results to at least four decimal places. Scientific notation is acceptable. For five extra points calculate the sample standard deviation for the last five digits of your university identification number and write the result in the upper right corner of this page. Correct calculations yield correct results. You may use Excel or a calculator. 4 points per item The average number of occurances within a defined sample space is equal to 10.86 Each occurance is assumed to be an independent event and the probability of an occurance is the same throughout the entire sample space. Furthermore, each sample space is assumed to be an independent entity. Use this information to determine the probability of the following events Splaynit: why is P(x = 11) greater than P(x = 3)? P(x = 5) = P(x = 3)- P(x = 11) =

Solution

a)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    10.86      
          
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.024184093 [ANSWER]

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b)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    10.86      
          
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.004101098 [ANSWER]

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c)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    10.86      
          
x = the number of successes =    11      
          
Thus, the probability is          
          
P (    11   ) =    0.119270842 [ANSWER]

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Splaynit:

P(x=11) is greater than P(X = 3) because 11 is closer to the mean (10.86) than 3. The closer you are to the mean, the greater the probability of the event happening.