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The distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 72.6 miles/hour and a standard deviation of 4.78 miles/hour. \(^{56}\) (a) What percent of passenger vehicles travel slower than 80 miles/hour? (b) What percent of passenger vehicles travel between 60 and 80 miles/hour? (c) How fast do the fastest \(5 \%\) of passenger vehicles travel? (d) The speed limit on this stretch of the I-5 is 70 miles/hour. Approximate what percentage of the passenger vehicles travel above the speed limit on this stretch of the I-5.

Find the standard deviation of the distribution in the following situations. (a) MENSA is an organization whose members have IQs in the top \(2 \%\) of the population. IQs are normally distributed with mean 100 , and the minimum IQ score required for admission to MENSA is 132 . (b) Cholesterol levels for women aged 20 to 34 follow an approximately normal distribution with mean 185 milligrams per deciliter \((\mathrm{mg} / \mathrm{dl})\). Women with cholesterol levels above \(220 \mathrm{mg} / \mathrm{dl}\) are considered to have high cholesterol and about \(18.5 \%\) of women fall into this category.

A poll conducted in 2013 found that \(52 \%\) of U.S. adult Twitter users get at least some news on Twitter. \(^{59}\) The standard error for this estimate was \(2.4 \%\), and a normal distribution may be used to model the sample proportion. Construct a \(99 \%\) confidence interval for the fraction of U.S. adult Twitter users who get some news on Twitter, and interpret the confidence interval in context.

A poll conducted in 2013 found that \(52 \%\) of U.S. adult Twitter users get at least some news on Twitter, and the standard error for this estimate was \(2.4 \%\). Identify each of the following statements as true or false. Provide an explanation to justify each of your answers. (a) The data provide statistically significant evidence that more than half of U.S. adult Twitter users get some news through Twitter. Use a significance level of \(\alpha=0.01\). (b) Since the standard error is \(2.4 \%\), we can conclude that \(97.6 \%\) of all U.S. adult Twitter users were included in the study. (c) If we want to reduce the standard error of the estimate, we should collect less data. (d) If we construct a \(90 \%\) confidence interval for the percentage of U.S. adults Twitter users who get some news through Twitter, this confidence interval will be wider than a corresponding \(99 \%\) confidence interval.