The student body of a large university consists of 30% Business majors. A random sample of 20 students is?

The student body of a large university consists of 30% Business majors. A random sample of 20 students is selected. What is the probability that exactly 10 are business majors?


a. .0008


b. .0039


c. .0308


d. .0479


e. None of the above

The student body of a large university consists of 30% Business majors. A random sample of 20 students is?
Because this is a relatively small sample, you can approximate the answer using the Binomial probability distribution binomialpdf(n,p,k) with n=20 and p=0.3 and k=10. You can get a fairly precise answer using a scientific calculator.





Alternatively you could use a table for the cumulative binomial probability distribution, as found in the appendices of most statistics textbooks, in which case the answer is the difference binomialcdf(20,0.3,10) - binomialcdf(20,0.3,9) which is equal to 0.983-0.952 or 0.031, which would correspond to answer choice C.