A recent Census Bureau survey showed that 42 of individuals

A recent Census Bureau survey showed that 42% of individuals, ages 25 and older, have completed four years of college. Suppose a random sample of 25 individuals, ages 25 and older, are selected. Based on this information, generate a cumulative binomial probability distribution and answer the following questions:

1. Find the probability that the number of people who have completed four years of college differs by greater than 3 from the mean.

2. Find the probability that greater than 4 people have completed four years of college.

3. Find the probability that exactly 15 people have not completed four years of college.

4. Find the probability that no less than 11 people have completed four years of college.

5. Find the probability that more than 30% but at most 60% of the people have completed four years of college.

6. Find the probability that at least 15 people have not completed four years of college.

7. Find the probability that no more than 9 people have completed four years of college.

Solution

1) P(7.5<x<13.5) = P(7<x<14) = 0.3465-0.0611 = 0.2854

2) P(X>4)=0.9945

3) P(X=25-15=10) =0.1579

4) P(x>=11) = 0.4956

5) P(30%<x<60%) = P(7.5<x<15)

= P(7<x<15)

= 0.9465-0.0495

= 0.8970

6) P(x<25-15=10) =0.3465

7)

= 0.3465