# MATHEMATICS

37. A researcher is interested in the lengths of Salvelinus fontinalis (brook trout), which are known to be approximately Normally distributed with mean 80 centimeters and standard deviation 5 centimeters. To help preserve brook trout populations, some regulatory standards need to be set limiting the size of fish that can be caught. To ensure that the shortest 8% of the brook trout get thrown back, the lower cut-off should be set at 75.00 centimeters. 87.03 centimeters. 72.95 centimeters. 80.00 centimeters. 38. The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg. Twenty-five percent of adult men with cirrhosis have a total body protein of at least 9.87 kg. 9.73 kg. 9.70 kg. 9.60 kg. 39. The amount of cholesterol in a person’s body produced by their liver and other cells is proposed to be Normally distributed with mean 75% and standard deviation 0.5%. The probability that a person produces more than 76.7% of the cholesterol in their body is 0.9997. 1. 0.0006. 0.0003. 40. A national survey by Gallup interviewed 1014 adults and found that they had consumed on average 4.2 alcoholic beverages in the past seven days. Considering a sample of 1014 adults a large sample, which of the following is TRUE? By the central limit theorem, the 1014 weekly number of drinks obtained in the sample are approximately Normally distributed. By the law of large numbers, the results of this study are 1014 times less variable than if only one American adult had been asked. By the law of large numbers, the average weekly number of drinks from repeated samples of size 1014 is approximately Normally distributed. By the central limit theorem, the average weekly number of drinks from repeated samples of size 1014 is approximately Normally distributed. 41. The fact that the sample mean doesn’t tend to over- or under-estimate the population mean makes the sample mean consistent. a statistic. unbiased. efficient. 42. You plan to randomly select 10 students from your campus and ask them how many minutes they exercised in the past seven days. The distribution of values taken by the average exercising time in all possible samples of size 10 is the variance of the exercising time values. probability distribution of exercising times. population parameter. sampling distribution of average exercising times. 43. The variability of a statistic is described by the spread of its sampling distribution. vagueness in the wording of the question used to collect the sample data. amount of bias present. stability of the population it describes. 44. The pH measurements of water specimens from various locations along a given river basin are Normally distributed with mean 8 and standard deviation 0.3. You take water specimens from 4 randomly selected locations on this river basin. Use the 68–95–99.7 rule to answer this question. What is the range of average pH measurements that make up roughly the middle 95% of the sampling distribution for random samples of 4 specimens? 7.7 to 8.3 7.4 to 8.6 7.85 to 8.15 7.925 to 8.075 45. The distribution of total body protein in adult men with liver cirrhosis is approximately Normal with mean 9.8 kg and standard deviation 0.1 kg. If you take a random sample of 25 adult men with liver cirrhosis, what is the probability that their average total body protein is between 9.75 and 9.85 kg?

0.3829

0.0796

0.0062

0.9876

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