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1 STAT 307 Homework #4 Spring 2008 Due Monday 3/24/08 Note: URI - All questions should be handed in. - Selected QUESTIONS would be graded. 1. Find the area under the standard normal curve that lies to the right of a. -1.07 2. b. 1.56 d. 4.2 Determine the area under the standard normal curve that lies between a. -2.18 and 1.44 c. 0.59 and 1.51 3. c. 0 b. -2 and -1.5 d. 1.1 and 4.2 Find the area under the standard normal curve that lies a. either to the left of -2.12 or to the right of 1.67 b. either to the left of 0.63 or to the right of 1.54. 4. Obtain the following z-scores. (Choose closest value. If halfway, then interpolate). a. z0.20 b. z0.005 5. In 1905, R. Pearl published the article “Biometrical Studies on Man. I. Variation and Correlation in Brain Weight”. According to the study, brain weights of Swedish men are normally distributed with a mean of 1.40 kg and a standard deviation of 0.11 kg. Obtain the percentage of 2 Swedish men who have brain weights a. between 1.5 kg and 1.70 kg. b. less than 1.6 kg. c. Determine the quartiles of the brain weights of Swedish men. d. Obtain the 20th percentile of the brain weights of Swedish men. 3 6. Using the data in problem 5 above. a. Determine the sampling distribution of the sample mean for samples of size 3. b. Repeat part (a) for samples of size 12. c. Construct graphs for the original distribution and for the sampling distributions for the mean brain weights for samples of size 3 and 12. Label the distribution accordingly. If you use Excel, then use the mathematical formula for a normal random variable with appropriate mean and standard deviation. A range of X values from 1 to 2 in steps of 0.1 will suffice. Overlay all three curves on the same graph. d. Is it necessary to assume that brain weights of Swedish men are normally distributed to answer parts (a) and (b)? Explain your answer. e. Determine the percentage of all samples of three Sweedish men that have mean brain weights within 0.1 kgs of the population mean brain weight of 1.40 kg. f. 7. Repeat part (e) for sample of size 12. Some studies of Alzheimer’s disease (AD) have shown an increase in CO2 production in patients with the disease. In one such study the following CO2 values were obtained from 7 neocortical biopsy samples from AD patients: 1009 1280 1180 1255 1547 2352 1080. 4 (Could use Excel to answer parts (a) and (b) of the question. Work to two decimal places.) a. Find the normal scores associated with the observed sampled values. b. Find the Normal Probability Plot of the data above. c. Comment on the normality of the data. Is there any hint of outliers in the data? What about skewness? Explain.