At a local community college 55 of students who enter the co

At a local community college, 55% of students who enter the college as freshmen go on to graduate. Four freshmen are randomly selected.

What is the probability that none of them graduates from the local college? (Round your intermediate calculations and final answer to 4 decimal places.)

What is the probability that at most three will graduate from the local college? (Round your intermediate calculations and final answer to 4 decimal places.)

Solution

a)

P(none) = (1-0.55)^4 = 0.04100625 [ANSWER]

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b)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    4      
p = the probability of a success =    0.55      
x = the maximum number of successes =    3      
          
Then the cumulative probability is          
          
P(at most   3   ) =    0.90849375 [ANSWER]

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c)

E(x) = n p = 4*0.55 = 2.2 [ANSWER]

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