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Each year thousands of high school students take either the SAT or the ACT, standardized tests used in the college admissions process. Combined SAT Math and Verbal scores go as high as \(1600,\) while the maximum ACT composite score is \(36 .\) since the two exams use very different scales, comparisons of performance are difficult. A convenient rule of thumb is \(S A T=40 \times A C T+150 ;\) that is, multiply an ACT score by 40 and add 150 points to estimate the equivalent SAT score. An admissions officer reported the following statistics about the ACT scores of 2355 students who applied to her college one year. Find the summaries of equivalent SAT scores. Lowest score \(=19 \quad\) Mean \(=27\) Standard deviation \(=3\) \(\mathrm{Q}^{3}=30 \quad\) Median \(=28 \quad\) IQR \(=6\)

A town's January high temperatures average \(36^{\circ} \mathrm{F}\) with a standard deviation of \(10^{\circ},\) while in July the mean high temperature is \(74^{\circ}\) and the standard deviation is \(8^{\circ} .\) In which month is it more unusual to have a day with a high temperature of \(55^{\circ} ?\) Explain.

The winning scores of all college men's basketball games for the \(2011-12\) season were approximately normally distributed with mean 77.5 points and standard deviation 12.5 points. a) Draw the Normal model for winning scores. b) What interval of winning scores would be the central \(95 \%\) of all winning scores for the \(2011-12\) season? c) About what percent of the winning scores should be less than 65 points? d) About what percent of the winning scores should be between 65 and 102 points? e) About what percent of the winning scores should be over 102 points?