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PubH 6002: Biostatistical Applications for Public HealthQuiz 2Student Name: _________________________Instructions : This quiz consists of 11 MC questions. While this quiz is designed to take 35minutes, you have 2 hours to complete it. Work individually! You may use your own formula sheets containing relevant hand-written notes as well as a standard or scientific calculator. Toreceive full credit, you must show all of your work. Good luck!1.A forestry study found that the diameter of trees in a forest is normally distributed with mean34 cm with a standard deviation of 8 cm. A group of 4 trees will be used as timber if the average of the 4 trees’ diameter is not too thick or too thin. Specifically, it is desired for the mean diameter to be between 30 and 40 cm in diameter. Find the probability that a randomly chosen group of 4 trees can be used as timber. a.1.5b.-1c..7745d..9332e.0.1586oWe are given the following information: oTree diameter is normally distributed,population meanμ= 34, andpopulation standard deviationσ= 8N = 4.oLet X= tree diameter.oWe are asked to find P(30 < ´X< 40).oApply the formula z= (´X– μ)/(σ/√n), and use the z-table to find the correct probability.oP(30 < ´X< 40) = P((30-34)/4 < Z < (40-34)/4) = P(-1 < Z < 1.5) = P(Z < 1.5) – P(Z < -1) = P(Z < 1.5) – P(Z > 1) Line 3 follows from Line 2 by the symmetry of the normal distribution. P(Z < 1.5) = .9332 column AP(Z > 1) = .1586 column BFinal Answer = .9332-.1587 = .7745 (C)
For questions 2-5, refer to the following information: A study is conducted to test thehypothesis that people with glaucoma have higher than average blood pressure. The study includes 15 people with glaucoma whose average SBP is 125 mm Hg. The sample variance calculated from these 15 people was 1024. The distribution of SBP appears to be bell-shaped. You need to construct a 90% confidence interval for the true mean SBP among people with glaucoma. To help you do so, answer each of the following questions.