244 CHAPTER 5 Normal Probability Distributions 38. Milk Consumption You are performing a study about weekly per capita milk consumption. A previous study found weekly per capita milk consumption to be normally distributed, with a mean of 48.7 fluid ounces and a standard deviation of 8.6 fluid ounces. You randomly sample 30 people and record the weekly milk consumptions shown below. 40 45 54 41 43 31 47 30 33 37 48 57 52 45 38 65 25 39 53 51 58 52 40 46 44 48 61 47 49 57 (a) Draw a frequency histogram to display these data. Use seven classes. Do the consumptions appear to be normally distributed? Explain. (b) Find the mean and standard deviation of your sample. (c) Compare the mean and standard deviation of your sample with those of the previous study. Discuss the differences. Computing and Interpreting z-Scores In Exercises 39 and 40, (a) find the z-score that corresponds to each value and (b) determine whether any of the values are unusual. 39. Stanford-Binet IQ Scores The test scores for the Stanford-Binet Intelligence Scale are normally distributed with a mean score of 100 and a standard deviation of 16. The test scores of four students selected at random are 98, 65, 106, and 124. (Source: StanfordBinetTest.com) 40. SAT Scores The test scores for students who took the SAT (without the essay) are normally distributed with a mean score of 1051 and a standard deviation of 211. The test scores of four students selected at random are 1050, 960, 870, and 1440. (Source: College Board) Finding Probability In Exercises 41– 46, find the probability of z occurring in the shaded region of the standard normal distribution. If convenient, use technology to find the probability. 41. −0.625 z 0 42. 1.96 z 0 43. −2.125 z 0 44. z 0 0.8 45. −1 1 z 0 46. 1.68 z 0
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