## Binomial probability

• Question 1

Sixty percent of the students applying to a university are accepted. Using the binomial probability tables or Excel, what is the probability that among the next 18 applicants:

1. At least 8 will be accepted?
2. Exactly 10 will be accepted?
3. Exactly 5 will be rejected?
4. Fifteen or more will be accepted?
5. Determine the expected number of acceptances.
6. Compute the standard deviation.

Question 2

Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6.

1. What is the probability that a randomly selected exam will have a score of at least 71?
2. What percentage of exams will have scores between 89 and 92?
3. If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?

*** Describe what you looked up on the table or show your computations for this assignment.

• For these project assignments throughout the course you will need to reference the data in the ROI Excel spreadheet. Download it here.

Using the ROI data set:

1. If we select 6 colleges from a major and then record whether they are of ‘School Type’ ‘Private’ or not, is this experiment a binomial one? Why or why not?
2. For each of the 2 majors determine if the ‘Annual % ROI’ appears to be normally distributed. This will involve your histogram from Week 1.  If your histogram was not correctly done, you must correct it before analyzing results.  Follow these steps.   1.  For each major, put in your corrected histogram.   2.  Look at the normal probability graph’s shape in your textbook.  3.  Compare the shapes.  4.  Calculate measures of central tendency (mean and median) and list them.   5.  By using the measures of central tendency and your “shape comparison,”  justify your conclusion if the Annual % ROI is normally distributed.  Report on each of these with charts and calculations to justify your answers.