The credit card industry has determined that about 65 of col

The credit card industry has determined that about 65% of college students will be late making a minimum payment when paying their credit card every year at least once. If 10 randomly selected students who own a credit card is selected. Find:

8. What is the mean and standard deviation of college students who are late at least once in a year?

a) 1.5 ; 2.45 b) 6.5 ; 1.51 c) 8.5 ; 3.25 d) 8.5 ; 3.58 e) 6.5 ; 3.58

9. What is the probability that at most 2 of the ten selected are late with their credit card payment?

a) 0.1123 b) 0.0455 c) 0.9929 d) 0.9550 e) 0.0048

10. What is the probability that more than 7 are late with their credit card payment?

a) 0.2522 b) 0.7478 c) 0.2616 d) 0.7895 e) 0.7484

Solution

8.

Mean = n p = 10*0.65 = 6.5 [OPTION B]

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9.

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.65      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.004821265 = 0.0048 [OPTION E]

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10.

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.65      
x = our critical value of successes =    7      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   7   ) =    0.738392609
          
Thus, the probability of at least   8   successes is  
          
P(more than   7   ) =    0.261607391 = 0.2616 [OPTION C]