Question

4 The Sampling Distributions of Means and Proportions The Central Limit Theorem] Suggested Reading #6 (The Central Limit Theorem) 41 Ponder this and calculate: Consider all possible random samples of 5 in a class of 28 many different samples are there? Show your work (not as tedious as it appears) Note: Please continue to use the algebraic notation, as discussed in class, to obtain the answer e.9. Px<54) or P (x> 112)-1-P(x< 112)-1-Pizs ete. 4.2 A nurse supervisor has found that staff nurses, on the average, complete a certain task in 42 minutes. If the times required to complete the task are approximately normally distributed with a stand ard deviation of 5 minutes, find: d) What if the distribution of task times was not normally distributed. Compute the probability thata randomly drawn sample of 36 nurses would complete the task, on average, in less than 40.5 minutes In a sentence or two, explain why you used the formula you did. 4.3.2 A study (The National Health and Nutrition Examination Survey) reported an estimated mean serun cholesterol level of 183 for women aged 20-29 years. The estimated standard deviation was approximately 37, Use these estimates as the mean μ and standard deviation σ for the U.S. population. If a simple random sample of size 60 is drawn from this population, find the probability that the sample mean serm cholesterol level wil1 be: (a) Below 175 (b) Greater than 190. Normal Approximation to the Binomial: 4.5.3 In the 1999-2000 NHANES report, researchers estimated that 64 percent of U.S. aduits ages 20-74 were overweight or obese (overweight: BMI 25-29, obese: BMI 30 or greater). Use this estimate as the population proportion for U.S. adults ages 20-74. If 125 subjects are selected at random from the population, what is the probability that 70 percent or more would be found to be overweight or obese? OPTIONAL Answer:0.0808 4.5.4 Gallagher et al. reported on a study to identify factors that influence women's attendance at cardiac rehabilitation programs. They found that by 12 weeks post-discharge, only 64 percent of eligible women attended such programs. Using 64 percent as an estimate of the attendance percentage of all eligible women, find the probability that in a sample of 45 women selected random from the population of eligible women less than 50 percent would attend programs. For continuous measurements, which should always be smaller, the standard deviation of the population of measurements or the standard error of a sample mean, drawn from this populati and why? 4.6

Answer 1

4.3.2 175-133 乙〈 ち 二10.0475 !90-18 37