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Question : A set of exam scores is 80, 75, 85, 90, 100, 70, 60. The standard deviation equals : 2163570

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

1) A set of exam scores is 80, 75, 85, 90, 100, 70, 60. The standard deviation equals

A) √(50)

B) √(20)

C) √(10)

D) 7

E) none of these

2) The table below is the probability table for a random variable X. Find E(X), Var(X), and the standard deviation of X.

A) E(X) = -0.2; Var(X) = 2.16; standard deviation of X =1.47

B) E(X) = -0.2; Var(X) = 2.22; standard deviation of X =1.49

C) E(X) = -0.2; Var(X) = 0; standard deviation of X = 0

D) E(X) = -0.2; Var(X) = 4; standard deviation of X =2

E) none of these

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

3) The table below is the probability table for a random variable X. Find E(X).

Enter just a reduced fraction of form (a/b).

4) The table below is the probability table for a random variable X. Find Var(X).

Enter just a reduced fraction of form (a/b).

5) The table below is the probability table for a random variable X. Find the standard deviation of X.

Enter just a real number rounded off to two decimal places.

6) The table below is the probability table for a random variable X. Find E(X).

Enter just a real number rounded off to two decimal places.

7) The table below is the probability table for a random variable X. Find Var(X).

Enter just a real number rounded off to two decimal places.

8) The table below is the probability table for a random variable X. Find the standard deviation of X.

Enter just a real number rounded off to two decimal places.

9) The table below is the probability table for a random variable X. Find E(X), Var(X), and the standard deviation of X.

Enter just three real numbers all rounded off to two decimal places: a, b, c representing the three quantities in the order requested above, separated by commas (no labels).

10) A car dealer records the number of Mercedes sold each week. During the past 50 weeks, there were 15 weeks with no sales, 20 weeks with one sale, 10 weeks with two sales, and 5 weeks with three sales. Let X be the number of Mercedes sold in a week selected at random from the past 50 weeks. Compute E(X). Enter just a real number rounded off to one decimal place (no label).

11) A student taking five courses keeps a record of the number of assignments due each day in all her courses. Over the course of the 60-day semester she finds on 20 days no assignments are due, on 15 days an assignment is due in one course, on 15 days an assignment is due in two courses, on 9 days an assignments is due in three courses and once during the semester she has an assignment due in 4 courses. If X is the number of assignments due on a day selected at random from the semester, find E(X).

Is E(X) = 0⋅(1/3) + 1⋅(1/4) + 2⋅(1/4) + 3⋅(3/20) + 4⋅(1/60) the correct answer?

Enter "yes" or "no".

12) The riders of the New Town Elementary school bus consists of 5 five year olds, 3 six year olds, 10 eight year olds, 1 nine year old, 4 eleven year olds and a twelve year old. A child is selected at random and her age is noted. Let X be the outcome. Find E(X). Enter just a reduced fraction of form (a/b) (no label).

13) A carnival game costs $2 to play. A player draws a ball at random from a sack containing 1 white ball, 2 blue balls, 3 red balls, and 4 yellow balls. The payoff for drawing a particular color ball is as follows: white pays $5, blue pays $4, red pays $3 and yellow pays nothing. If X is the amount of money a player wins. Calculate E(X). Enter just a real number rounded off to two decimal places (no label).

14) John would like to place a two dollar bet on his favorite racehorse, Black Velvet. He can bet that Black Velvet will win or show (finish in the top three horses). If he bets correctly that Black Velvet wins, he wins $20. If he bets correctly that Black Velvet shows, he wins $7. John figures Black Velvet has a 20% chance of winning and a 70% chance of showing. If X is the amount of money John wins if he bets Black Velvet will win and Y is the amount of money he wins if Black Velvet will show, find E(X) and E(Y) . Enter just two real numbers rounded off to two decimal places in the order given above representing dollars (no units).

15) A Christmas tree grower anticipates a profit of $80,000 in a usual season. There is however a 10% chance of pine bark beetle infestation in which case 70% of the trees are destroyed and profit is reduced to $24,000. The grower can spray for beetles at the beginning of the season at a cost of $7,000. Compute E(X). Enter just an integer rounded off to the nearest thousand.

16) Joe has a lawn mowing job. If he completes the work he earns $40. But there is a 30% chance it may rain, in which case he won't finish the job. He can pay Jane $20 to help him and ensure that he finishes the job. If X is the amount Joe will get if he does not get Jane to help, calculate E(X) and thus decide whether Joe should hire Jane or not. (If it rains, assume Joe will make no money and if Joe hires Jane assume they will be able to finish the job before it rains. Enter your answer exactly as a,b where a is an integer representing E(X) in dollars (no units), and b is either "yes" or "no" answering the question "should Joe hire Jane?", separated by a comma.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine whether the function is a probability density function over the given interval.

17) f(x) = (1/4), 8 ≤ x ≤ 12

A) Yes

B) No