Assume that a procedure yields a binomial distribution with

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.

Solution

8.

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 =    0.25      
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.263671875 [ANSWER]

**********************

9.

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    22      
p = the probability of a success =    0.06      
x = the maximum number of successes =    1      
          
Then the cumulative probability is          
          
P(at most   1   ) =    0.616301699 [ANSWER]

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!