A university found that 30 of its students withdraw without

A university found that 30% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.

Compute the probability that 2 or fewer will withdraw (to 4 decimals).
  

Compute the probability that exactly 4 will withdraw (to 4 decimals).
  

Compute the probability that more than 3 will withdraw (to 4 decimals).
  

Compute the expected number of withdrawals.

Solution

a)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.3      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.035483132 [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 =    20      
p = the probability of a success =    0.3      
x = the number of successes =    4      
          
Thus, the probability is          
          
P (    4   ) =    0.130420974 [ANSWER]

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c)

Note that P(more than x) = 1 - P(at most x).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    20      
p = the probability of a success =    0.3      
x = our critical value of successes =    3      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   3   ) =    0.107086805
          
Thus, the probability of at least   4   successes is  
          
P(more than   3   ) =    0.892913195 [ANSWER]

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d)

E(x) = n p = 20*0.3 = 6 [ANSWER]