mathematics

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  Question 1   

12 Points

What is the average?

3 4 5 8

 

2

 

4

 

5

 

10

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  Question 2   

12 Points

What is the median of these figure skating ratings?

6.0   6.0   7.0   7.0   7.0   8.0   9.0

 

6.0

 

7.0

 

7.1

 

8.0

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  Question 3   

11 Points

Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:

Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50)

Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50)

What is Jo’s margin of error, rounded to the nearest whole number? (The formula is  )

 

10

 

20

 

50

 

529

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  Question 4   

11 Points

A media personality argues that global temperatures are not rising, because every year an increase is reported such as 0.08 degrees C. The difference from the previous year is less than the margin of error of about 0.15 degrees C, so that difference should be ignored. What is a strong counterargument?

 

Even 0.08 degrees is a lot and thus should be  considered.

 

The margin of error is just extra information and  thus can be ignored.

 

The difference with any previous decade is much  greater than the margin of error.

 

0.15 - 0.08 is 0.07, which is still an increase and  thus should be considered.

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  Question 5   

11 Points

An article reports that blue eyed people earn less than brown eyed people, with these numbers: average blue-eyed salary $35,000, average brown-eyed salary $37,000, p-value 0.45. Based on that reported p-value, and using the common definition of "statistical significance," which is the case?

 

The results are nowhere near to being statistically  significant.

 

The results are almost but not quite statistically  significant.

 

The results are just barely statistically  significant.

 

The results are strongly statistically significant.

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  Question 6   

11 Points

A group of 10 people is choosing a chairperson and vice-chairperson. They put all 10 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?

 

19

 

90

 

100

 

10! (10 factorial)

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  Question 7   

11 Points

A lock consists of 3 dials, where each dial has 4 letters. What is the probability of guessing the right combination in one try?

 

1/7

 

1/12

 

1/24

 

1/64

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  Question 8   

11 Points

About 8% of the U.S. population catches the flu each season. Assuming everyone has equal probability of catching the flu, about what are the odds of catching the flu in a given season?

 

1 in 8

 

1 in 12

 

1 in 18

 

1 in 80

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  Question 9   

11 Points

Kay has an 80% probability of making a free-throw in basketball, and each free-throw is independent. Kay gets to take 2 free-throws, and must make both to win the game. What is the probability that Kay's team will win the game?

 

64%

 

80%

 

88%

 

160% (so 100%)

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  Question 10   

11 Points

A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 0.9, $50 0.1. Over many weeks, what is a worker's expected weekly bonus?

 

(10 + 50) / 2 = $30

 

10×0.9 + 50×0.1 = $14

 

(10×0.9 + 50×0.1) / 2 = $7

 

(10 + 50) / 10 = $6

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  Question 11   

11 Points

Estimate the average by first rounding to the nearest 1,000:

1,000 2,300 2,600

 

2000 

 

3000

 

4200

 

6000

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  Question 12   

11 Points

Both sets of values have an average of 13. Is Set A's standard deviation smaller, larger, or about the same as Set B's? (Note: This question can be answered by knowing the concept of standard deviation, without actually computing the standard deviation).

Set A: 1 2 3 23 24 25

Set B: 8 10 12 14 16 18

 

Smaller

 

Larger 

 

About the same

 

Unable to tell

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  Question 13   

11 Points

If a study determines the difference in average salary for subpopulations of people with blue eyes and people with brown eyes is NOT significant, then the populations of blue-eyed people and brown-eyed people are ________ different salaries. 

 

unlikely to have 

 

very likely to have

 

guaranteed to have

 

guaranteed to not have

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  Question 14   

11 Points

How many values are in the range 35 to 95? 

 

62

 

61 

 

60

 

59

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  Question 15   

11 Points

A restaurant will select 1 card from a bowl to win a free lunch. Jo puts 5 cards in the bowl. The bowl has 100 cards. What are the odds of Jo winning a free lunch? 

 

1/5

 

1/10

 

1/20 

 

1/500

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  Question 16   

11 Points

A medication states that the odds of having an allergic reaction are 1 in 50. What is that probability states as a percent? 

 

1%

 

2% 

 

4%

 

5%

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  Question 17   

11 Points

A slot machine has 3 dials. Each dial has 30 positions, one of which is "Jackpot". To win the jackpot, all three dials must be in the "Jackpot" position. Assuming each play spins the dials and stops each independently and randomly, what are the odds of one play winning the jackpot? 

 

1/30 = 0.03 or 3%

 

3/(30+30+30) = 3/90 = 0.33 or 33%

 

3/(30×30×30) = 3/27000 = 0.0001 or 0.01%

 

1/(30×30×30) = 1/27000 = 0.00003 or  0.003%  

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  Question 18   

11 Points

In any given year, a factory has a 20% probability of having an accident. About every how many years might the factory expect to have an accident? 

 

Every 1 year

 

Every 2 years

 

Every 5 years 

 

Every 20 years

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