Complete the following questions relative to the following s

Complete the following questions relative to the following statement:  A soda-filling machine is known to under fill an incorrect amount of soda on 5% of the cans it fills.
   1.   Find by the appropriate method, the probability that the machine under fills 1 can in a set of 15 cans.
   2.   Find by the appropriate method, the probability that the machine under fills no more than 3 cans in a set of 15 cans.
   3.   Find by the appropriate method, the probability that the machine under fills no more than 3 cans in a set of 10 cans
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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 =    15      
p = the probability of a success =    0.05      
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.365756234 [answer]

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2.

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    15      
p = the probability of a success =    0.05      
x = the maximum number of successes =    3      
          
Then the cumulative probability is          
          
P(at most   3   ) =    0.994532741 [answer]

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3.

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.05      
x = the maximum number of successes =    3      
          
Then the cumulative probability is          
          
P(at most   3   ) =    0.998971502 [answer]