91影视

A deck of cards contains $52$cards, of which $4$are aces. You are offered the following wager: Draw one card at random from the deck. You win $\backslash (10$if the card drawn is an ace. Otherwise, you lose $\backslash )1$. If you make this wager very many times, what will be the mean amount you win?

(a) About 鈭�$\backslash (1$, because you will lose most of the time.

(b) About $\backslash )9$, because you win $\backslash (10$but lose only $\backslash )1$.

(c) About 鈭�$\backslash (0.15$; that is, on average you lose about $15$cents. (d) About $\backslash )0.77$; that is, on average you win about $77$cents.

(e) About $\$0$, because the random draw gives you a fair bet.

Suppose a student is randomly selected from your school. Which of the following pairs of random variables are most likely independent?

(a)$X=$student鈥檚 height; $Y$= student鈥檚 weight

(b) $X$= student鈥檚 IQ;$Y$ = student鈥檚 GPA

(c) $X$= student鈥檚 PSAT Math score;$Y$ = student鈥檚 PSAT Verbal score

(d)$X$= average amount of homework the student does per night;$Y$ = student鈥檚 GPA

(e)$X$ = average amount of homework the student does per night; $Y$ = student鈥檚 height

Spell-checking software catches 鈥渘onword errors,鈥� which result in a string of letters that is not a word, as when 鈥渢he鈥� is typed as 鈥渢eh.鈥� When undergraduates are asked to write a 250-word essay (without spell-checking), the number X of nonword errors has the following distribution:

(a) Write the event 鈥渁t least one nonword error鈥� in terms of $X$. What is the probability of this event?

(b) Describe the event $X鈮�2$in words. What is its probability? What is the probability that$X<2$?

The deck of $52$cards contains $13$hearts. Here is another wager: Draw one card at random from the deck. If the card drawn is a heart, you win $2$. Otherwise, you lose $1$. Compare this wager (call it Wager 2) with that of the previous exercise (call it Wager $1$). Which one should you prefer?

(a) Wager $1$, because it has a higher expected value.

(b) Wager $2$, because it has a higher expected value.

(c) Wager $1$, because it has a higher probability of winning.

(d) Wager $2$, because it has a higher probability of winning. (e) Both wagers are equally favorable

Better readers?($1.3$) Did students have higher reading scores after participating in the chess program? Give appropriate statistical evidence to support your answer.

Refer to the previous Check Your Understanding (page 390 ) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined $X=$the number of Patti's correct guesses.

1. Find ${渭}_{\mathrm{X}}$. Interpret this value in context.

A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let $蠂$= the number of cars sold and $纬$= the number of cars leased during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distributions of $蠂$and $纬$are as follows:

顿别铿乶别$D=X-Y$

Find and interpret $渭D$.

Chess and reading ($4.3$) If the study found a statistically signi铿乧ant improvement in reading scores, could you conclude that playing chess causes an increase in reading skills? Justify your answer

Predicting posttest scores($3.2$) What is the equation of the linear regression model relating posttest and pretest scores? 顿别铿乶别 any variables used.

Refer to the previous Check Your Understanding (page 390) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined $X=$the number of Patti's correct guesses.

3. What's the probability that the number of Patti's correct guesses is more than $2$standard deviations above the mean? Show your method.