An increasing number of consumers believe they have to look

An increasing number of consumers believe they have to look out for themselves in the marketplace. According to a survey conducted by the Yankelovich Partners for USA WEEKEND magazine, 60% of all consumers have called an 800 or 900 telephone number for information about some product. Suppose a random sample of 19 consumers is contacted and interviewed about their buying habits.

Appendix A Statistical Tables (Round your answers to 3 decimal places when calculating using Table A.2.)

a. What is the probability that 11 or more of these consumers have called an 800 or 900 telephone number for information about some product?

b. What is the probability that more than 14 of these consumers have called an 800 or 900 telephone number for information about some product?

c. What is the probability that fewer than 7 of these consumers have called an 800 or 900 telephone number for information about some product?

Solution

a)

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 =    19      
p = the probability of a success =    0.6      
x = our critical value of successes =    11      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   10   ) =    0.33251896
          
Thus, the probability of at least   11   successes is  
          
P(at least   11   ) =    0.66748104 [ANSWER]

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b)

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    19      
p = the probability of a success =    0.6      
x = our critical value of successes =    14      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   14   ) =    0.930386292
          
Thus, the probability of at least   15   successes is  
          
P(more than   14   ) =    0.069613708 [ANSWER]

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c)

Note that P(fewer than x) = P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    19      
p = the probability of a success =    0.6      
x = our critical value of successes =    7      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   6   ) =    0.011562944
          
Which is also          
          
P(fewer than   7   ) =    0.011562944 [ANSWER]