Quantitative Reasoning - What is the average

Quantitative Reasoning

1.) What is the average of the following numbers?

2, 5, 8, 1

2.) What is the median of these figure skating ratings?

5.0 6.0 7.0 7.5 8.0 9.0 10.0

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

· Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50)

· Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50)

What is Val’s margin of error, rounded to the nearest whole number? (The formula is 1.96 (std dev)

4.) A media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?

5.) An article reports that men over 6 feet tall earn more than men under 6 feet, with these numbers: average 6 foot plus male’s salary $55,000, average male’s salary under 6 foot tall of $47,000, with a p-value of 0.45. Based on that reported p-value, and using the common definition of "statistical significance," which is the case?

6.) A group of 16 people is choosing a chairperson and vice-chairperson. They put all 16 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?

7.) A lock consists of 4 dials, where each dial has 6 letters. What is the probability of guessing the right combination in one try?

8.) A place kicker in pro football has a 77% probability of making a field goal over 40 yards, and each attempted field goal is independent. If the kicker made his first two but missed his third attempt and is now trying for his fourth field goal of the game to win in overtime, what is the probability that his team will win the game?

9.) A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 - 0.75, $50 - 0.25. Over many weeks, what is a worker's expected weekly bonus?

10.) Estimate the average by first rounding to the nearest 100:

120, 230, 455, 175

11.) 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: 9 10 11 14 16 18

12.) If a study determines the difference in average salary for subpopulations of mechanical engineers and civil engineers is NOT significant, then the subpopulations of mechanical and civil engineers are ________ different salaries.

13.) How many integers are in the range 17 to 118?

14.) A restaurant will select 1 card from a bowl to win a free lunch. Jimmy puts 10 cards in the bowl. The bowl has a total of 150 cards in it when they do the drawing. What are the odds of Jimmy winning a free lunch?

15.) A medication states that the odds of having an allergic reaction are 2 in 200. What is that probability states as a percent?

16.) A slot machine has 3 dials. Each dial has 40 positions, two of which are "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?

17.) Database A contains 40 data items and is made up with an equal number of the values of 0 and 100 and has a mean of 50. Database B also has 40 entries made up equally of the values 49 and51 and also has a mean of 50. Which database will have the smaller value for its standard deviation?

18.) Using a standard six-sided die, Janice rolled either a 2 or a 5on the last 6 rolls of the die. What is the probability of Janice rolling a 2or a 5 on her 7th toss of the die?

19.) A bag of the same size small balls contains 6 blue balls, 5 red balls, 5 yellow balls, and 4 green balls. What is the probability of selecting a blue or green ball on the first draw?

20.) In any given year, a factory has a 10% probability of having a serious accident. About every how many years might the factory expect to have an accident?