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Find $\alpha$ for a 90% confidence interval.

Make a 90% confidence interval for a parameter, y, with point estimate $ŷ=-1.5$, & margin of error $E=3.25$.

Find the critical value, $z_{\frac{\alpha }{2}}$, for a 80% confidence interval.

Determining Sample Size. Assume that each sample is a simple random sample obtained from a normally distributed population.

You want to estimate for the population of diastolic blood pressures of air traffic controllers in the United States. Find the minimum sample size needed to be 95% confident that the sample standard deviation s is within 1% of σ. Is this sample size practical?

Ergonomics. Exercises 9–16 involve applications to ergonomics, as described in the Chapter Problem.

Designing Manholes According to the website www.torchmate.com, “manhole covers must be a minimum of 22 in. in diameter, but can be as much as 60 in. in diameter.” Assume that a manhole is constructed to have a circular opening with a diameter of 22 in. Men have shoulder widths that are normally distributed with a mean of 18.2 in. and a standard deviation of 1.0 in. (based on data from the National Health and Nutrition Examination Survey).

a. What percentage of men will fit into the manhole?

Interpreting Normal Quantile Plots. In Exercises 5–8, examine the normal quantile plot and determine whether the sample data appear to be from a population with a normal distribution.

Ages of Presidents The normal quantile plot represents the ages of presidents of the United States at the times of their inaugurations. The data are from Data Set 22 “Presidents” in Appendix B.

Determining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a distribution that is roughly bell-shaped.

Taxi Trips The distances (miles) traveled by New York City taxis transporting customers, as listed in Data Set 32 “Taxis” in Appendix B