Posted: November 29th, 2022

*1. *A simple random sample of pages from *Merriam-Webster’s Collegiate Dictionary, was obtained. *Listed below are the number of defined words

on those pages, and they are arranged in order. Construct the boxplot and include the 5 number summary. Can you say anything about the distribution of words per page in a Merriam-Webster Collegiate Dictionary? If not, why not?

34 63 36 79 39 53 43 73 51 62

2. Nola Ochs recently became the oldest college graduate when she graduated at the age of 95. If her age is included with the ages of 25 typical students at the time of their graduation, how much of an effect will her age have on the mean, median, standard deviation, and range?

3. Death certificates provide data on the causes of death. Which of the three main measures of center is appropriate here? Explain your answer.

4. SAT scores have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which is relatively better: a score of 1030 on the SAT test or a score of 14.0 on the SAT test? Why?

5. A certain virus afflicted the families in 3 adjacent houses in a row of 12 houses. If three houses were randomly chosen from a row of 12 houses, what is the probability that the 3 houses would be adjacent? Is there a reason to believe that the virus is contagious?

6. A meteorologist in Chicago recorded the number of days of rain during a 30-day period. If the random variable x is defined as the number of days of rain, does x have a binomial distribution? Explain your answer.

7. In a case in Riverhead, New York, nine different crime victims listened to voice recordings of five different men. All nine victims identified the same voice as that of the criminal. If the voice identifications were made by random guesses, find the probability that all nine victims would select the same person. Does this constitute reasonable doubt?

8. According to FBI data 24.9% of robberies are cleared with arrests. A new detective is assigned to 10 different robberies.

a. What is the probability that at least one is cleared with an arrest?

b. What is the probability that the detective clears all 10 robberies with an arrest?

c. What should we conclude if the detective clears all 10 robberies with an arrest?

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**Extra Point:**

The annual sunspot numbers are found for a recent sequence of 24 years. The data are sorted, then it is found that the mean is 81.09, the standard deviation is 50.69, the minimum is 8.6, the first quartile is 29.55, the median is 79.95, the third quartile is 123.3, and the maximum is 157.6. What potentially important characteristic of these annual sunspot numbers is lost when the data are replaced by the sorted values?

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