s 20 points Suppose that there is a 085 probability that a r

s. (20 points) Suppose that there is a 0.85 probability that a randomly selected adult knows what Twitter is. a. Use the binomial probability formula to find the probability of getting exactly 3 adults who knorw what Twitter is when 4 adults are randomly selected. b Use the binomial probability formala and the addition rule to f ind the probability of getting 0 or 1 adults who know what Twitter is when 4 adults are randomly selected. c. Use your caleulator to find the probability of getting exactly 20 adults who know what Twitter is when 30 adults are randomly selected. d. Use your calculator to find the probability of getting at least 15 adults who know what Twitter is when 30 adults are randomly selected.

Solution

8. Suppose that there is a 0.85 probability that a randomly selected adult knows what Twitter is.

a)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    4      
p = the probability of a success =    0.85      
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.368475 [ANSWER]

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b)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    4      
p = the probability of a success =    0.85      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.00050625

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    4      
p = the probability of a success =    0.85      
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.011475

Thus,

P(0 or 1) = P(0) + P(1) = 0.00050625 + 0.011475 = 0.01198125 [ANSWER]

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c)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    30      
p = the probability of a success =    0.85      
x = the number of successes =    20      
          
Thus, the probability is          
          
P (    20   ) =    0.006715271 [ANSWER]

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d)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    30      
p = the probability of a success =    0.85      
x = our critical value of successes =    15      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   14   ) =    1.14474E-06
          
Thus, the probability of at least   15   successes is  
          
P(at least   15   ) =    0.999998855 [ANSWER]

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