The grade distribution for scores on a final exam is shown in the following stem-and-leaf plot:

Stem	Leaves
2	7
3
3
4	01
4	899
5	4
5	5
6	122
6	58
7	00124
7	9
8	0044
8	5679
9	00223334
9	5788

Units: 9|8 = 98%

(a) What is the shape of the grade distribution?

(b) How many students earned 90% or better?

(c) How many students earned less than 60%?

For the following exercise, use the following table, which gives the monthly returns for the Janus Growth and Income S Fund, the S&P 500, and the sector returns for large growth funds.

Month	Janus	S&P	Large Growth	Month	Janus	S&P	Large Growth
MAY 2013	$1.33$	$2.34$	$2.63$	NOV 2011	$-0.8$	$-0.22$	$-1.06$
APR 2013	$3.01$	$1.93$	$1.25$	OCT 2011	$14.17$	$10.93$	$11.78$
MAR 2013	$4.26$	$3.75$	$3.19$	SEP 2011	$-10.38$	$-7.03$	$-8.45$
FEB 2013	$1.54$	$1.36$	$0.65$	AUG 2011	$-7.94$	$-5.43$	$-6.67$
JAN 2013	$4.8$	$5.18$	$4.75$	JUL 2011	$-2.81$	$-2.03$	$-1.27$
DEC 2012	$1.8$	$0.91$	$0.52$	JUN 2011	$-1.21$	$-1.67$	$-1.5$
NOV 2012	$0.56$	$0.58$	$1.95$	MAY 2011	$-1.07$	$-1.13$	$-1.27$
OCT 2012	$-1.87$	$-1.85$	$-3.01$	APR 2011	$3.67$	$2.96$	$2.91$
SEP 2012	$1.84$	$2.58$	$2.3$	MAR 2011	$-0.24$	$0.04$	$0.37$
AUG 2012 12	$2.77$	$2.25$	$3.27$	FEB 2011	4	$3.43$	$3.27$
JUL 2012	$2.11$	$1.39$	$0.47$	JAN 2011	$2.38$	$2.37$	$1.83$
JUN 2012	$2.8$	$4.12$	$2.6$	DEC 2010	$4.93$	$6.68$	$5.54$
MAY 2012	$-7.19$	$-6.01$	$-7.37$	NOV 2010	$-1.18$	$0.01$	$1.08$
APR 2012	$-0.94$	$-0.63$	$-0.7$	OCT 2010	$3.65$	$3.8$	$4.62$
MAR 2012	$2.32$	$3.29$	$3.37$	SEP 2010	$9.31$	$8.92$	$10.81$
FEB 2012	$5.33$	$4.32$	$5.34$	AUG 2010	$-4.22$	$-4.51$	$-4.72$
JAN 2012	$6.45$	$4.48$	$6.31$	JUL 2010	$6.02$	$7.01$	$6.73$
DEC 2011	$0.43$	$1.02$	$-1.14$	JUN 2010	$-3.92$	$-5.23$	$-5.62$

Find the mean monthly return for the Large Growth funds. Convert this value to the annual return.

How are z-scores found for normal distributions with $\mu \neq 0$ or $\sigma \neq 1$?

For the following exercise,

(a) write a frequency distribution;

(b) draw a histogram.

The data come from a random sample of 40 companies from the S&P 500.

Draw a stem-and-leaf plot for the following data. (Round to the nearest units place.)

$$\begin{array}{rrrr}39.9 & 9.7 & 9.2 & 33.3 \\ 1.4 & 10.0 & 4.0 & 57.7 \\ 5.0 & 4.4 & 28.6 & 10.4 \\ 8.1 & 4.1 & 3.6 & 2.6 \\ 65.9 & 1.8 & 3.9 & 12.5 \\ 3.6 & 2.9 & 19.4 & 11.7 \\ 6.7 & 1.7 & 15.2 & 18.1 \\ 8.2 & 10.9 & 4.2 & 2.2 \\ 24.4 & 4.4 & 16.5 & 16.3 \\ 1.6 & 10.5 & 9.6 & 5.2\end{array}$$

Use the following table for the following table, which lists expenditures (in billions of dollars with the exception of Parks and Recreation, which is in millions of dollars) for a random sample of seven states. Find the range and standard deviation among the seven states for each category of government expenditure.

	State
Type of Expenditure	GA	IL	LA	MI	NH	OH	PA
Education	24.9	34.8	12.0	29.1	$3.6$	$32.8$	$35.1$
Public Welfare	9.7	17.8	6.4	12.9	2.0	18.4	24.5
Hospitals	5.1	2.6	4.6	3.5	0.1	4.0	3.0
Health	2.0	3.1	0.9	3.8	0.1	3.9	3.8
Highways	3.4	8.2	2.9	3.7	0.7	4.8	8.6
Police Protection	2.2	4.6	1.4	2.4	0.3	3.3	3.1
Fire Protection	1.0	2.3	0.6	2.3	0.2	1.8	0.7
Parks and Recreation	964	2552	709	725	107	1226	1194

Education

Which of the following has the greater probability: drawing an ace and a ten-card (ten, jack, queen, or king) from a standard deck of $52$ playing cards, or drawing an ace and a ten-card from two standard decks of playing cards?

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. Find the probability of drawing an ace and a king in either order.

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. Are the outcomes on the two cards independent? Why?

A bag contains 10 red, 6 green, 7 yellow, and 5 orange jelly beans. What is the probability of randomly choosing a red jelly bean, replacing, randomly choosing another red jelly bean, replacing, and then randomly choosing an orange jelly bean?

M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the distribution of colors for plain M&M candies is $$ \begin{matrix} \text{Color } & \text{Purple} & \text{Yellow} & \text{Red} & \text{Orange} & \text{Green} & \text{Blue} & \text{Brown}\\ \text{Percentage} & \text{20\\%} & \text{20\\%} & \text{20\\%} & \text{10\\%} & \text{0.1} & \text{0.1} & \text{0.1}\\ \end{matrix} $$ Suppose you have a large bag of plain M&M candies and you choose one candy at random. Find P(green candy or blue candy). Are these outcomes mutually exclusive? Why?

Multiplication Rule Given P(A)=0.2 and P(B)=0.4:

(a) If $A$ and $B$ are independent events, compute $P(A$ and $B)$. (b) If $P(A \mid B)=0.1$, compute $P(A$ and $B)$.

Given $P(A)=0.6$ and $P(B)=0.2$, do the following.

$(a)$ If $A$ and $B$ are independent events, compute $P(A\cap B)$.

$(b)$ If $P(A\mid B)=0.3$, compute $P(A\cap B)$.

Find the mean for the following data set. Round to the nearest tenth.

Earthquakes on the Richter scale:

3.5, 4.2, 5.8, 6.3, 7.1, 2.8, 3.7, 4.2, 4.2, 5.7

If two events $A$ and $B$ are independent and you know that $P(A)=0.3$, what is the value of $P(A \mid B)$ ?