A salesperson contacts prospective customers by telephone, and estimates that 25

Question

A salesperson contacts prospective customers by telephone, and estimates that 25% of all telephone calls results in a sale. The salesperson makes 8 telephone calls. Find the probability that (No need to simplify) Exactly 5 telephone calls result in a sale. No telephone calls results in a sale. At least 2 of the 8 telephone calls result in a sale. How many arrangements are there of all the letters in ILLINOIS? Give a single integer as your answer. How many arrangements are there of all the letters in SUNLIGHT? Give a single integer as your answer. How many arrangements are there of all the letters in STATISTICS? Give a single integer as your answer

Explanation / Answer

17.

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 =    8      
p = the probability of a success =    0.25      
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.023071289 [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 =    8      
p = the probability of a success =    0.25      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.100112915 [ANSWER]

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c)

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 =    8      
p = the probability of a success =    0.25      
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   1   ) =    0.367080688
          
Thus, the probability of at least   2   successes is  
          
P(at least   2   ) =    0.632919312 [ANSWER]

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