PubHlth 540 – Fall 2011 Introductory Biostatistics Page 1 of 2 Unit 5 – The Normal Distribution Practice Problems Due: Monday November 7, 2011 1. Before you begin: This exercise gives you practice in calculating probabilities under the standard normal curve. See lecture notes for unit 5 pp 12-18. A good url to use is http://davidmlane.com/hyperstat/z_table.html Find the proportion of observations from a standard normal distribution that satisfies each of the following statements. a. Z < 2.85 b. Z > 2.85 c. Z > -1.66 d. -1.66 < Z < 2.85 e. Z < -2.25 f. Z > -2.25 g. Z > 1.77 h. -2.25 < Z < 1.77 hw_normal.docPubHlth 540 – Fall 2011 Introductory Biostatistics Page 2 of 2 2. Before you begin: This exercise gives you practice in calculating probabilities under normal curves with non-zero mean and non-unit variance. The same url will work for this exercise too. It is http://davidmlane.com/hyperstat/z_table.html The height, X, of young American women is distributed normal with mean μ=65.5 and standard deviation σ=2.5 inches. Find the probability of each of the following events. a. X < 67 b. 64 < X < 67 3. Before you begin: This exercise gives you additional practice in calculating probabilities under normal curves with non-zero mean and non-unit variance. Suppose the distribution of GRE scores satisfies the assumptions of normality with a mean score of μ=600 and a standard deviation of σ=80. a. What is the probability of a score less than 450 or greater than 750? b. What proportion of students have scores between 450 and 750? c. What score is equal to the 95th percentile? 4. Before you begin: Ditto The Chapin Social Insight Test evaluates how accurately the subject appraises other people. In the reference population used to develop the test, scores is normally distributed with mean μ=25 and standard deviation σ=5. The range of possible scores is 0 to 41. a. What proportion of the population has scores below 20 on the Chapin test? b. What proportion has scores below 10? c. How high a score must you have in order to be in the top quarter of the population in social insight? 5. Before you begin: This exercise is purposely more thoughtful and asks you to think a bit about the meaning of the ideas in unit 5. There is not an explicit example that you can mimic. Just give it a try! A normal distribution has mean μ=100 and standard deviation σ=15 (for example, IQ). Give limits, symmetric about the mean, within which 95% of the population would lie: a. Individual observations. b. Means of 4 observations. c. Means of 16 observations. d. Means of 100 observations. e. Write down an expression for the width of the limits symmetric about the mean, within which 95% of the population of means of samples of size n would lie.