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The average 20 - to 29 -year-old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while the average 20 - to 29 -year-old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 67-inch man or a 62 -inch woman?

The following data represent the age of U.S. presidents on their respective inauguration days (through Barack Obama). $$ \begin{array}{lllllllll} \hline 42 & 47 & 50 & 52 & 54 & 55 & 57 & 61 & 64 \\ \hline 43 & 48 & 51 & 52 & 54 & 56 & 57 & 61 & 65 \\ \hline 46 & 49 & 51 & 54 & 55 & 56 & 57 & 61 & 68 \\ \hline 46 & 49 & 51 & 54 & 55 & 56 & 58 & 62 & 69 \\ \hline 47 & 50 & 51 & 54 & 55 & 57 & 60 & 64 & \\ \hline \end{array} $$ (a) Find the five-number summary. (b) Construct a boxplot. (c) Comment on the shape of the distribution.

The highest batting average ever recorded in Major League Baseball was by Ted Williams in 1941 when he hit \(0.406 .\) That year, the mean and standard deviation for batting average were 0.2806 and \(0.0328 .\) In 2014 Jose Altuve was the American League batting champion, with a batting average of \(0.341 .\) In \(2014,\) the mean and standard deviation for batting average were 0.2679 and \(0.0282 .\) Who had the better year relative to his peers, Williams or Altuve? Why?

The data below represent the age of the mother at the time of her first birth for a random sample of 30 mothers. $$ \begin{array}{llllll} \hline 21 & 35 & 33 & 25 & 22 & 26 \\ \hline 21 & 24 & 16 & 32 & 25 & 20 \\ \hline 30 & 20 & 20 & 29 & 21 & 19 \\ \hline 18 & 24 & 33 & 22 & 23 & 25 \\ \hline 17 & 23 & 25 & 29 & 25 & 19 \\ \hline \end{array} $$ (a) Construct a box plot of the data. (b) Use the box plot and quartiles to describe the shape of the distribution.

The following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in Sullivan's Statistics course. Compute the range, sample variance, and sample standard deviation time. $$ 60.5,128.0,84.6,122.3,78.9,94.7,85.9,89.9 $$

A manufacturer of bolts has a quality control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The quality-control engineer knows that the bolts coming off the assembly line have a mean length of \(8 \mathrm{~cm}\) with a standard deviation of \(0.05 \mathrm{~cm} .\) For what lengths will a bolt be destroyed?

The following data represent the flight time (in minutes) of a random sample of seven flights from Las Vegas Nevada, to Newark, New Jersey, on United Airlines. Compute the range and sample standard deviation of flight time. $$ 282,270,260,266,257,260,267 $$

A certain type of concrete mix is designed to withstand 3000 pounds per square inch (psi) of pressure. The concrete is poured into casting cylinders and allowed to set for 28 days. The concrete's strength is then measured. The following data represent the strength of nine randomly selected casts (in psi). Compute the mean, median, and mode strength of the concrete (in psi). $$ 3960,4090,3200,3100,2940,3830,4090,4040,3780 $$

Explain the meaning of the following percentiles. Source: National Center for Health Statistics. (a) The 5 th percentile of the weight of males 36 months of age is \(12.0 \mathrm{~kg}\). (b) The 95 th percentile of the length of newborn females is \(53.8 \mathrm{~cm}\)

The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a "flipped" classroom. The "flipped" classroom is one where the content is delivered via video and watched at home, while class time is used for homework and activities. $$ \begin{array}{llllllll} \hline \text { Traditional } & 70.8 & 69.1 & 79.4 & 67.6 & 85.3 & 78.2 & 56.2 \\\ & 81.3 & 80.9 & 71.5 & 63.7 & 69.8 & 59.8 & \\ \hline \text { Fipped } & 76.4 & 71.6 & 63.4 & 72.4 & 77.9 & 91.8 & 78.9 \\ & 76.8 & 82.1 & 70.2 & 91.5 & 77.8 & 76.5 & \end{array} $$ (a) Which course has more dispersion in exam scores using the range as the measure of dispersion? (b) Which course has more dispersion in exam scores using the standard deviation as the measure of dispersion? (c) Suppose the score of 59.8 in the traditional course was incorrectly recorded as \(598 .\) How does this affect the range? the standard deviation? What property does this illustrate?