# Grantham University Week 3 Standard Deviation and Statistics Questions

Question 1 – Binomials

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 9 applicants:

1. Exactly 6 will be accepted? (Hint – for 1-4, I strongly suggest using the link to the table if you are not strong in Excel)
2. At least 8 will be accepted?
3. Exactly 5 will be rejected?
4. Four or more will be accepted?
5. Determine the expected number of accepted students. Remember you are talking about people. Work is required. Hint: Notations and Symbols has a formula for this. Expected…
6. Compute the standard deviation.- Make sure you have looked at page 245. Work is required. Another hint: Notations and Symbols has the formula for variance right under the formula for the expected value . Standard deviation is the square root of the variance. If you use the formula to find the variance, then all you have to do is take the square root…

Here is a website with binomial tables in case you prefer this table to the book’s table.

https://www.dummies.com/education/math/statistics/figuring-binomial-probabilities-using-the-binomial-table/

Question 2 – Normal distribution

Scores on a recent national statistics exam were normally distributed with a mean of 50 and a standard deviation of 3.

1. What is the probability that a randomly selected exam will have a score of at least 58? Work is required. Here’s a hint. You calculate the z score and you look at the table to get the probability. That value is the probability to the LEFT of the z score. “At least” means you have to look to the RIGHT of the z score. What does your last step have to be???
2. In the question above, you should have calculated a z score. Why isn’t the z score the answer to the question?
3. What percentage of exams will have scores between 46 and 54? Work is required.
4. What percentage of exams will be two standard deviations from the mean? (Find this in the book in words – do not do math)
5. If the top 6% of test scores receive merit awards, what is the lowest score eligible for an award? Work is required.

A hint from Dr. Klotz: This is my favorite online z table.

http://www.z-table.com/

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