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(solution) MATH 1324 Quiz 7 Show all work in the space provided. Credit will

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MATH 1324

Quiz 7

Show all work in the space provided. Credit will be given only for work that is clear and readable.

Please staple all pages together before turning in the quiz.

29. Use the following list of numbers to compute the statistics:

83, 89, 88, 84, 82, 86, 89, 84, 86, 83, 85, 87, 87, 83 mean _____________

median _____________

mode _____________

range _____________

sample standard deviation _____________

population standard deviation _____________ When rounding is needed, give answers correct to 4 digits after the decimal point.

30. Using the same data from problem 1, group the data into the classes 82 ? 84, 85 ? 87, and 88 ? 90

and compute the statistics.

Classes

Midpoint

frequency

82 ? 84

85 ? 87

88 - 90

mean _____________

sample standard deviation _____________

population standard deviation _____________

When rounding is needed, give answers correct to 4 digits after the decimal point.

31. Find the value of c such that the area of the shaded region below is A = .8172 .

3. ___________________ 32. A regular size sack of a certain candy is supposed to contain 2.17 g of candy. Assume the weights of

the sacks are normally distributed. Suppose the machine that fills these sacks is set so that on the

average, a sack contains 2.25 g with a standard deviation of 0.1 g.

a) The tick-marks on the x-axis are the standard z-scores. In the blanks below each z-score, write the

corresponding x-values using the mean and standard deviation given in the problem. ?3 ?2 ?1 0 1 2 3 x1=________ x2=________ x3=________ x4=________ x5=________ x6=________ x7=________ b) What fraction of the sacks will be under weight? (give answer as a decimal)

b) ___________________ c) If 15,000 sacks are produced, how many will be underweight?

c) ___________________

d) What fraction of the sacks will weigh less than 2 g? (give answer as a decimal)

d) ___________________ e) If 15,000 sacks are produced, how many will weigh less than 2 g?

e) ___________________ f) What frraction of the sacks will weigh more thann 2.3 g? (give answer as a decimal)

f) _____________________ g) If 15,0000 sacks are produced, hoow many will weigh

w

more thhan 2.3 g? g) _____________________ g (give answ

wer as a decim

mal)

h) What fraction of thee sacks will weeigh betweenn 2.2 and 2.5 g?

h) _____________________ i) If 15,0000 sacks are produced,

p

how

w many will weigh

w

betweenn 2.2 and 2.5 g?

g

i) _____________________

ments that apply to the pictture.

33. For each picture, list the letter(s) of the statem

a)) You will neeed to find onlyy one z-score.

b)) You will neeed to find two z-scores.

c)) You will neeed to use the table to look up

u one area.

d)) You will neeed to use the table to look up

u two differeent areas.

e)) The probabbility will equall the area founnd in the tablee.

f) The probability will equal the differencee between 1 and

a the area found

f

in the taable.

g)) The probabbility will equall the differencce between the two areas foound in the taable. beetween__________ left __________ right __________ 34. A law firm has 7 senior partners and 12 junior partners. If 3 people from the firm are selected to sit on

a committee, what is the expected number of senior partners on that committee? You must show the

complete probability distribution and all answers should be exact fractions and not decimal numbers.

5. P(no seniors) = _____

P(one senior) = _____

P(two seniors) = _____

P(three seniors) = _____

expected number of seniors _____ 35. After paying $4 to play, a single fair die is rolled and you are paid back the number of dollars

corresponding to the number of dots facing up except if you roll a one in which case you lose an additional

$3. What is the expected value of the game?

6. I would expect to ________ _____ and the game _____ fair.

(win or lose) (amount) (is or is not) 36. Two coins are flipped. You win $2 if either 2 heads or 2 tails turn up; you lose $3 if a head and a tail

turn up. What is the expected value of the game?

7. I would expect to _______ _____ and the game _____ fair.

(win or lose) (amount)

(is or is not)

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