Workshop 4

The Normal Distribution

Name: _______________________________________

Date Completed: _____________

Provide all solutions, answers and requested outputs after each question.

Question 1: The normal distribution of IQ scores is 100 with a standard deviation of 15.
                    If an individual with a tested IQ of 70 or below is considered mentally retarded,
                    what percentage of the population would be classified retarded?

Question 2: If the range of "average" IQ scores is 90 to 110, what percentage of the population is
                    considered average in intelligence?

Question 3. Assume a random sample, X is taken from the following distribution, compute
                    their z-scores and use the standard normal distribution table to compute their
                    cumulative probabilities.

                    X = {12, 14, 23, 13, 15, 20, 14, 18, 17, 15}

Question 4. For a population with mean of m = 70, a score of 62 corresponds to a z-score of z = -2.00.
                    What is the population standard deviation? (hint, use the z-score formula and
                    solve for the unknown or SD)

Question 5. Bill earned a score of X = 73 on an English test with a mu = 65 and the s = 8. John, his best friend,
                    earned a score of X = 63 on a math test with a m = 57 and s = 3. Who should the better grade?
                    Explain your answer. (Hint: use the concept of percentile rank)

Question 6. Use a statistical software the compute the z-scores for all the scores of an experiment for weight gain,
in pounds, of the following 12 females:

Subjects Mary Ann Sue Lisa Kim Jen Wendy Rose Toni Frans Beth June
Weight Changes






-2.9 -0.1



-5.3 -3.8


Question 7. A number of years ago the mean and the standard deviation on the Graduate Record Exam
                    (GRE) for all people taking the exam were 489 and 126 respectively.
                    What percentage of students would be expected to have a score for 600 of less?
                    (This is called the percentile rank of 600)

Question 8. Scores on the SAT standardized exam has a normal distribution with mean = 500 and SD = 100.
                    What is the minimum score needed to be in the top 20% on the SAT exam?
                    (Hint, find the 80 percentile for the SAT).

Question 9. To find the 95% Confidence Interval (the interval, symmetrical about the mean where 95% of the
                    distribution lies) for a sample distribution with mean, M = 50 and standard deviation, SD = 10,
                    we must find the 2.5 percentile and then the 97.5 percentile. What is the 95%

Question 10:   (a) Use a statistical package and compute the z-score for the pass4th variable of the ODE.csv dataset.
                        (b) How many scores are greater than z = +2? Paste your output here.