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In one definition of hypertension, three categories are used: individuals whose systolic blood pressures are less than 140 , those with blood pressures between 140 and 160 , and those with blood pressures over 160 . For males between the ages of eighteen and twenty-four, systolic blood pressures are normally distributed with a mean equal to 124 and a standard deviation equal to 13.7. Suppose a random sample of ten individuals from that particular demographic group are examined. What is the probability that six of the blood pressures will be in the first group, three in the second, and one in the third?

A disgruntled Anchorage bush pilot, upset because his gasoline credit card was cancelled, fires six air-to-surface missiles at the Alaskan pipeline. If a missile lands anywhere within twenty yards of the pipeline, major structural damage will be sustained. Assume that the probability function reflecting the pilot's expertise as a bombardier is the expression $$ f_{Y}(y)= \begin{cases}\frac{60+y}{3600} & -60

One hundred unordered samples of size 2 are drawn without replacement from an urn containing six red chips and four white chips. Test the adequacy of the hypergeometric model if zero whites were obtained 35 times; one white, 55 times; and two whites, 10 times. Use the \(0.10\) decision rule.

Show that the common belief in the propensity of babies to choose an inconvenient hour for birth has a basis in observation. A maternity hospital reported that out of one year's total of 2650 births, some 494 occurred between midnight and 4 A.M. (179). Use the goodness-of-fit test to show that the data are not what we would expect if births are assumed to occur uniformly in all time periods. Let \(\alpha=0.05\).

From 1837 to 1932 , the U.S. Supreme Court had forty-eight vacancies. The table in the next column shows the number of years in which exactly \(k\) of the vacancies occurred. At the \(\alpha=0.01\) level of significance, test the hypothesis that these data can be described by a Poisson pdf. $$ \begin{array}{cc} \hline \text { Number of Vacancies } & \text { Number of Years } \\ \hline 0 & 59 \\ 1 & 27 \\ 2 & 9 \\ 3 & 1 \\ 4+ & 0 \\ \hline \end{array} $$

In rotogravure, a method of printing by rolling paper over engraved, chrome- plated cylinders, the printed paper can be flawed by undesirable lines called bands. Bands occur when grooves form on the cylinder's surface. When this happens, the presses must be stopped, and the cylinders repolished or replated. The following table gives the number of workdays a printing firm experienced between successive banding shutdowns (44). Fit these data with an exponential model and perform the appropriate goodness-of-fit test at the \(0.05\) level of significance. $$ \begin{array}{cc} \hline \text { Workdays Between Shutdowns } & \text { Number Observed } \\ \hline 0-1 & 130 \\ 1-2 & 41 \\ 2-3 & 25 \\ 3-4 & 8 \\ 4-5 & 2 \\ 5-6 & 3 \\ 6-7 & 1 \\ 7-8 & 1 \\ \hline \end{array} $$

A sociologist is studying various aspects of the personal lives of preeminent nineteenth-century scholars. A total of one hundred twenty subjects in her sample had families consisting of two children. The distribution of the number of boys in those families is summarized in the following table. Can it be concluded that the number of boys in two-child families of preeminent scholars is binomially distributed? Let \(\alpha=0.05\). $$ \begin{array}{lrrr} \hline \text { Number of boys } & 0 & 1 & 2 \\ \text { Number of families } & 24 & 64 & 32 \\ \hline \end{array} $$