For exercise 14 given a binomial situation with n 5 p 08

For exercise #1-4, given a binomial situation with n = 5 & p = 0.8 find: For exercises #5-8, given a binomial situation with n = 8 & p = 0.3 find: for exercises #9-12. given a binomial situation with n = 9 & p = 0.5 find: for exercises #13-16, given a binomial situation with n=12 & p 0.1 find: For exercises #17-20, say if the probability distribution is skewed left or symmetric or skewed

Solution

6.

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    8      
p = the probability of a success =    0.3      
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   ) =    0.99993439
          
Thus, the probability of at least   8   successes is  
          
P(more than   7   ) =    0.00006561 [answer]

9.

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 =    9      
p = the probability of a success =    0.5      
x = the number of successes =    4      
          
Thus, the probability is          
          
P (    4   ) =    0.24609375 [answer]

13.

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 =    12      
p = the probability of a success =    0.1      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.282429536 [answer]

15.

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 =    12      
p = the probability of a success =    0.1      
x = our critical value of successes =    3      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   2   ) =    0.889130022
          
Thus, the probability of at least   3   successes is  
          
P(at least   3   ) =    0.110869978 [answer]