Having troublewith random variables Assume that X is a binom

Having trouble....with random variables!

Assume that X is a binomial random variable with n = 6 and p = 0.68. Calculate the following probabilities. (Round your intermediate calculations and final answers to 4 decimal places.)

  a. P(X = 5)

  b. P(X = 4)

  c. P(X 4)

Solution

A)

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 =    6      
p = the probability of a success =    0.68      
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.279155245 [ANSWER]

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B)

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 =    6      
p = the probability of a success =    0.68      
x = the number of successes =    4      
          
Thus, the probability is          
          
P (    4   ) =    0.328417935 [answer]

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c)

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 =    6      
p = the probability of a success =    0.68      
x = our critical value of successes =    4      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   3   ) =    0.293559337
          
Thus, the probability of at least   4   successes is  
          
P(at least   4   ) =    0.706440663 [ANSWER]