A stemplot showing life expectancies of females in the nations of South America (Round to nearest year and use split stems.)

Construct the indicated stemplot from the data in the table below. Then write a brief interpretation of the stemplot.

LIFE EXPECTANCY BY GENDER FOR THE NATIONS OF SOUTH AMERICA

$$\begin{array}{lcc} \hline \text { Nation } & \text { Male } & \text { Female } \\ \hline \text { Argentina } & 71.9 & 78.8 \\ \text { Bolivia } & 61.5 & 66.7 \\ \text { Brazil } & 59.0 & 67.7 \\ \text { Chile } & 72.6 & 79.4 \\ \text { Colombia } & 66.7 & 74.6 \\ \text { Ecuador } & 68.5 & 74.3 \\ \text { Guyana } & 60.5 & 66.2 \\ \text { Paraguay } & 71.4 & 76.5 \\ \text { Peru } & 67.9 & 72.8 \\ \text { Suriname } & 69.0 & 74.4 \\ \text { Uruguay } & 72.1 & 79.0 \\ \text { Venezuela } & 70.3 & 76.6 \\ \hline \end{array}$$

Undergraduate students at Miami University in Oxford, Ohio, were surveyed in order to evaluate the effect of gender and price on purchasing a pizza from Pizza Hut. Students were told to suppose that they were planning to have a large two-topping pizza delivered to their residence that evening. The students had to decide between ordering from Pizza Hut at a reduced price of $\$ 8.49$ (the regular price for a large two-topping pizza from the Oxford Pizza Hut at the time was $\$ 11.49$ ) and ordering a pizza from a different pizzeria. The results from this question are summarized in the following contingency table:

$$\begin{aligned} &\qquad\qquad\qquad\qquad\text { PIZZERIA }\\ &\begin{array}{lccc} \text { GENDER } & \text { Pizza Hut } & \text { Other } & \text { Total } \\ \hline \text { Female } & 4 & 13 & 17 \\ \text { Male } & \underline{6} & \underline{12} & \underline{18} \\ \text { Total } & 10 & 25 & 35 \end{array} \end{aligned}$$

A subsequent survey evaluated purchase decisions at other prices. These results are summarized in the following contingency table:

$$\begin{array}{lcccc} & &\qquad{\text { PRICE }} \\ \text { PIZZERIA } & \$ 8.49 & \$ 11.49 & \$ 14.49 & \text { Total } \\ \hline \text { Pizza Hut } & 10 & 5 & 2 & 17 \\ \text { Other } & \frac{25}{35} & \frac{23}{28} & \frac{27}{29} & \\ \text { Total } & 35 & \frac{75}{92} \end{array}$$

Determine the $p$-value in the previous part and interpret its meaning.

The two-way table shows the gender and hair color of the students in a class.

$$\begin{array}{|c|c|c|c|} \hline & \text { Brown Hair } & \text { Blonde Hair } & \text { Red Hair } \\ \hline \text { Girl } & 3 & 6 & 3 \\ \hline \text { Boy } & 5 & 4 & 1 \\ \hline \end{array}$$

A student is chosen at random from the class. Find the probability that the student

(i) is a girl

(ii) has blonde hair

(iii) is a girl or has red hair

A stemplot showing the difference between female and male life expectancies in the nations of South America (Ise. unrounded data and do not split stems.)

Construct the indicated stemplot from the data in the table below. Then write a brief interpretation of the stemplot.

LIFE EXPECTANCY BY GENDER FOR THE NATIONS OF SOUTH AMERICA

$$\begin{array}{lcc} \hline \text { Nation } & \text { Male } & \text { Female } \\ \hline \text { Argentina } & 71.9 & 78.8 \\ \text { Bolivia } & 61.5 & 66.7 \\ \text { Brazil } & 59.0 & 67.7 \\ \text { Chile } & 72.6 & 79.4 \\ \text { Colombia } & 66.7 & 74.6 \\ \text { Ecuador } & 68.5 & 74.3 \\ \text { Guyana } & 60.5 & 66.2 \\ \text { Paraguay } & 71.4 & 76.5 \\ \text { Peru } & 67.9 & 72.8 \\ \text { Suriname } & 69.0 & 74.4 \\ \text { Uruguay } & 72.1 & 79.0 \\ \text { Venezuela } & 70.3 & 76.6 \\ \hline \end{array}$$

The U.S. National Science Foundation publishes data on doctoral degrees conferred in the document Science and Engineering Doctorate Awards. The following joint probability distribution summarizes the doctoral degrees conferred in the social sciences and psychology by gender during one year.

$$\begin{aligned} &\text { Field }\\ &\begin{array}{|c|c|c|c|} \hline \ {}{}{} & \begin{array}{c} \text { Social science } \\ F_1 \end{array} & \begin{array}{c} \text { Psychology } \\ F_2 \end{array} & \boldsymbol{P}\left(\boldsymbol{G}_{\boldsymbol{i}}\right) \\ \hline \begin{array}{c} \text { Male } \\ G_1 \end{array} & 0.300 & 0.119 & 0.419 \\ \hline \begin{array}{c} \text { Female } \\ G_2 \end{array} & 0.282 & 0.298 & 0.581 \\ \hline \boldsymbol{P}\left(F_j\right) & 0.582 & 0.418 & 1.000 \\ \hline \end{array} \end{aligned}$$

a. Find $P\left(G_1\right), P\left(F_1\right)$, and $P\left(G_1 \& F_1\right)$.

b. Use the special multiplication rule to determine whether events $G_1$ and $F_1$ are independent.

A stemplot showing life expectancies of males in the nations of South America (Round to nearest year and use split stems.)

Construct the indicated stemplot from the data in the table below. Then write a brief interpretation of the stemplot.

LIFE EXPECTANCY BY GENDER FOR THE NATIONS OF SOUTH AMERICA

$$\begin{array}{lcc} \hline \text { Nation } & \text { Male } & \text { Female } \\ \hline \text { Argentina } & 71.9 & 78.8 \\ \text { Bolivia } & 61.5 & 66.7 \\ \text { Brazil } & 59.0 & 67.7 \\ \text { Chile } & 72.6 & 79.4 \\ \text { Colombia } & 66.7 & 74.6 \\ \text { Ecuador } & 68.5 & 74.3 \\ \text { Guyana } & 60.5 & 66.2 \\ \text { Paraguay } & 71.4 & 76.5 \\ \text { Peru } & 67.9 & 72.8 \\ \text { Suriname } & 69.0 & 74.4 \\ \text { Uruguay } & 72.1 & 79.0 \\ \text { Venezuela } & 70.3 & 76.6 \\ \hline \end{array}$$

More people are staying single longer in the United States. The following table gives the percent of nevermarried adults, age 15 and over, by gender, for the years 1995 and 2013 . The growth has been approximately linear. Source: U.S.Census.

A steel beam ABC is simply supported at A and B and has an overhang BC of length L=150 mm . The beam supports a uniform load of intensity q=3.5 kN / m over its entire length of 450 mm.

The cross section of the beam is rectangular with width b and height 2 b. The allowable bending stress in the steel is $\sigma_{\text {allow }}=60$ MPa and its weight density is $\gamma=77.0 kN / m ^3$.

(a) Disregarding the weight of the beam, calculate the required width b of the rectangular cross section.

(b) Taking into account the weight of the beam, calculate the required width b.

Use the data in the table below to construct the indicated frequency table, using intervals 55.0-59.9, 60.0-64.9, 65.0-69.9, etc.

LIFE EXPECTANCY BY GENDER FOR THE NATIONS OF SOUTH AMERICA

$$\begin{array}{lcc} \hline \text { Nation } & \text { Male } & \text { Female } \\ \hline \text { Argentina } & 71.9 & 78.8 \\ \text { Bolivia } & 61.5 & 66.7 \\ \text { Brazil } & 59.0 & 67.7 \\ \text { Chile } & 72.6 & 79.4 \\ \text { Colombia } & 66.7 & 74.6 \\ \text { Ecuador } & 68.5 & 74.3 \\ \text { Guyana } & 60.5 & 66.2 \\ \text { Paraguay } & 71.4 & 76.5 \\ \text { Peru } & 67.9 & 72.8 \\ \text { Suriname } & 69.0 & 74.4 \\ \text { Uruguay } & 72.1 & 79.0 \\ \text { Venezuela } & 70.3 & 76.6 \\ \hline \end{array}$$

Life expectancies of females in the nations of South America

A wood beam A B on simple supports with span length equal to 9 ft is subjected to a uniform load of intensity 120 lb / ft acting along the entire length of the beam and a concentrated load of magnitude 8800 lb acting at a point 3 ft from the right-hand support. The allowable stresses in bending and shear, respectively, are 2500 psi and 150 psi.

(a) From the table in Appendix F, select the lightest beam that will support the loads (disregard the weight of the beam).

(b) Taking into account the weight of the beam (weight density $=35 lb / ft ^3$ ), verify that the selected beam is satisfactory, or, if it is not, select a new beam.

The cross section of a narrow-gage railway bridge is shown. The bridge is constructed with longitudinal steel girders that support the wood cross ties. The girders are restrained against lateral buckling by diagonal bracing, as indicated by the dashed lines.

The spacing of the girders is $s_1=50 in$. and the spacing of the rails is $s_2=30 in$. The load transmitted by each rail to a single tie is $P=1500 lb$. The cross section of a tie, shown in part (b) of the figure, has width $b=5.0 in$. and depth $d$.

Determine the minimum value of $d$ based upon an allowable bending stress of 1125 psi in the wood tie. (Disregard the weight of the tie itself.)

A survey of 1,520 Americans adults asked "Do you feel overloaded with too much information?" The results indicate that $23 \%$ of females feel information overload compared to $17 \%$ of males. The results are:

What conclusions can you reach from these analyses?

What does Mandela mean by "an actual South African reality"? The time for the healing of the wounds has come.... The time to build is upon us. We have, at last, achieved our political emancipation [freedom from bondage or control by others]. We pledge ourselves to liberate all our people from the continuing bondage [slavery] of poverty, deprivation [lack of materials necessary for survival]. suffering, gender and other discrimination. ... We have triumphed in the effort to implant [insert] hope in the breasts of the millions of our people. We enter into a covenant [binding agreement] that we shall build the society in which all South Africans, both black and white, will be able to walk tall, without any fear in their hearts, assured of their inalienable right to human dignity-a rainbow nation at peace with itself and the world. ...