The probability that a randomly chosen sales prospect will m

The probability that a randomly chosen sales prospect will make a purchase is 0.7. A salesperson talks to five prospects. What is the probability that he will make exactly four sales? What is the probability that he will make up to four sides? What is the expected number of sales?

Solution

1.

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 =    5      
p = the probability of a success =    0.7      
x = the number of successes =    4      
          
Thus, the probability is          
          
P (    4   ) =    0.36015 [ANSWER]

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2.

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    5      
p = the probability of a success =    0.7      
x = the maximum number of successes =    4      
          
Then the cumulative probability is          
          
P(at most   4   ) =    0.83193 [ANSWER]

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3.

E(x) = n p = 5*0.7 = 3.5 [ANSWER]