12th grade statistics and probability

Question 1

Ice-cream sales and sunburn cases are strongly correlated. Does this show that one causes the other?

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

Question 2

A game pays 2 points with probability 0.25, 8 points with probability 0.25, 7 points with probability 0.5. What is the expected number of points?

Answer 

Question 3

A charity game costs 5 to play. The chance of winning is 0.2 and the prize is 23 (the stake is kept). Is the game fair?

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

Question 4

It costs $1 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 5

The regression line is ŷ = 4.5x − 2. By how much does the predicted y change when x increases by 1?

Answer 

Question 6

For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 21 + 4x. Predict the score for 7 hours of revision.

Answer 

Question 7

A trial succeeds with probability 0.5. It is repeated 6 times independently. What is the probability of exactly 1 success? Round to 3 decimal places.

Answer 

Question 8

In a game you choose 4 different numbers from 1 to 18. Then 4 winning numbers are drawn. What is the probability that you match all 4? Give a fraction.

Answer (as a fraction)

Question 9

A regression line was found from data with x between 5 and 14 and strong correlation. How reliable is a prediction for x = 6?

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

Question 10

For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 1.9x. What does −1.9 tell you?

• A. Screen time causes 1.9 hours less sleep
• B. Each extra hour of screen time goes with about 1.9 fewer hours of sleep per week, on average
• C. A teenager with no screen time sleeps 1.9 hours
• D. The correlation coefficient is −1.9

Question 11

A raffle ticket costs 1 points. There is a 0.1 chance of winning 18 points. What is the expected gain per ticket (prize value minus cost)? It may be negative.

Answer 

Question 12

A correlation coefficient is r = −0.4. How would you describe the correlation?

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

Question 13

A data set has correlation coefficient r = −0.1. How would you describe the correlation?

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

Question 14

X is normally distributed with mean 60 and standard deviation 20. Find P(X < 44.6) to 3 decimal places.

Answer 

Question 15

A team of 2 is chosen at random from 3 girls and 5 boys. Find the probability that the team is all girls, as a fraction in simplest form.

Answer (as a fraction)

Question 16

Battery life is normally distributed with mean 161 minutes and standard deviation 18 minutes. Find the probability that a battery lasts between 134 and 177 minutes, to 3 decimal places.

Answer