Statistics questions

Question 1

Eighty 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 20 applicants:

  1. Exactly 10 will be accepted? Why is this number so low? (#4 might help)
  2. At least 14 will be accepted? (14 or more will be accepted)
  3. Exactly 5 will be rejected?
  4. Determine the expected number of acceptances.
  5. Compute the standard deviation. Make sure you are using the formula in the book specific to binomial problems.

Question 2

Scores on a recent national statistics exam were normally distributed with a mean of 88 and a standard deviation of 2.

  1. What is the probability that a randomly selected exam will have a score of at least 85?
  2. What percentage of exams will have scores between 89 and 92?
  3. If the top 5% of test scores receive merit awards, what is the lowest score eligible for an award?

Question 3

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. According to the textbook, what criteria are needed in a binomial experiment?
  • 2. If we select 10 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?
  • 3. According to the textbook, if data is normally distributed, and the mean is 10, what will the median be? What will the mode be?
  • 4. Find and insert a graph that shows the normal distribution with standard deviations (up to three standard deviations). Is a value in the data set more “special” if it is two or three standard deviations from the mean? Why? What are standard deviations telling you? How does the curve relate to this concept?
  • 5. For each of the 2 majors determine if the ‘Annual % ROI’ appears to be normally distributed. Consider the shape of the histogram and the measures of central tendency (mean and median) to justify your results. Report on each of these with charts and calculations to justify your answers.
  • 6.Continuing the theme of a highlighted box that you will use for your final project, summarize your analysis of whether or not the data in each graph is normally distributed. Why, given the context of our final project, is a normal distribution important?

 

 

Last Updated on February 10, 2019 by EssayPro