12th grade statistics and probability

Question 1

Children with bigger shoe sizes have better reading scores. Does this show that one causes the other?

• A. No: the correlation must be a calculation error
• B. Yes: strong correlation proves causation
• C. Yes, but only if r is above 0.9
• D. Not necessarily: a third factor, age, could explain both

Question 2

A correlation coefficient is r = −0.92. How would you describe the correlation?

• A. strong positive
• B. strong negative
• C. weak positive
• D. weak negative
• E. no linear correlation

Question 3

For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 1.3x. What does −1.3 tell you?

• A. Screen time causes 1.3 hours less sleep
• B. The correlation coefficient is −1.3
• C. A teenager with no screen time sleeps 1.3 hours
• D. Each extra hour of screen time goes with about 1.3 fewer hours of sleep per week, on average

Question 4

A game pays 8 points with probability 0.5, 2 points with probability 0.3, 3 points with probability 0.2. What is the expected number of points?

Answer 

Question 5

It costs $3 to play. You roll a fair die and win $9 if you roll a 5 or a 6. (Your stake is not returned.) What is the expected gain per game? Give the amount as a number; negative means a loss.

Answer 

Question 6

Battery life is normally distributed with mean 329 minutes and standard deviation 24 minutes. Find the probability that a battery lasts between 322 and 333 minutes, to 3 decimal places.

Answer 

Question 7

The regression line is ŷ = 3.5x + 29. By how much does the predicted y change when x increases by 1?

Answer 

Question 8

A regression line was found from data with x between 1 and 15 and strong correlation. How reliable is a prediction for x = 39?

• A. Reliable: it is interpolation within the data
• B. Unreliable: it is extrapolation beyond the data

Question 9

A raffle ticket costs 4 points. There is a 0.2 chance of winning 17 points. What is the expected gain per ticket (prize value minus cost)? It may be negative.

Answer 

Question 10

X is normally distributed with mean 114 and standard deviation 18. Find P(X < 87) to 3 decimal places.

Answer 

Question 11

Adult heights are normally distributed with mean 180 cm and standard deviation 6 cm. Find P(height > 194 cm) to 3 decimal places.

Answer 

Question 12

For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 17 + 3x. Predict the score for 8 hours of revision.

Answer 

Question 13

In a game you choose 3 different numbers from 1 to 17. Then 3 winning numbers are drawn. What is the probability that you match all 3? Give a fraction.

Answer (as a fraction)

Question 14

A data set has correlation coefficient r = 0.38. How would you describe the correlation?

• A. Strong positive
• B. Moderate positive
• C. Little or no linear correlation

Question 15

A charity game costs 4 to play. The chance of winning is 0.2 and the prize is 20 (the stake is kept). Is the game fair?

• A. Fair
• B. Favours the player
• C. Favours the organiser

Question 16

A trial succeeds with probability 0.3. It is repeated 6 times independently. What is the probability of exactly 5 successes? Round to 3 decimal places.

Answer