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Section 5.2 Exercises

(b) The sample result x is an unbiased estimator of the population truth \i no matter what size SRS the study chooses. Explain to someone who knows no statistics why a large sample gives morę trustworthy results than a smali sample.

5.30    Newly manufactured automobile radiators may have smali leaks. Most have no leaks, but some have 1, 2, or morę. The number of leaks in radiators madę by one supplier has mean 0.15 and standard deviation 0.4. The distribution of number of leaks cannot be normal because only whole-number counts are possible. The supplier ships 400 radiators per day to an auto assembly plant. Take x to be the mean number of leaks in these 400 radiators. Over several years of daily shipments, what rangę of values will contain the middle 95% of the many x’s?

5.31    The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test have a distribution that is approximately normal with mean ja — 300 and standard deviation ar = 35.

(a)    Choose one 12th-grader at random. What is the probability that his or her score is higher than 300? Higher than 335?

(b)    Now choose an SRS of four 12th-graders. What is the probability that