12th grade statistics and probability

Question 1

A game pays 5 points with probability 0.2, 3 points with probability 0.2, 1 points with probability 0.6. What is the expected number of points?

Answer 

Question 2

A raffle ticket costs 5 points. There is a 0.2 chance of winning 21 points. What is the expected gain per ticket (prize value minus cost)? It may be negative.

Answer 

Question 3

A team of 4 is chosen at random from 7 girls and 7 boys. Find the probability that the team is all girls, as a fraction in simplest form.

Answer (as a fraction)

Question 4

A regression line was found from data with x between 3 and 15 and strong correlation. How reliable is a prediction for x = 13?

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

Question 5

Adult heights are normally distributed with mean 154 cm and standard deviation 9 cm. Find P(height > 162 cm) to 3 decimal places.

Answer 

Question 6

It costs $1 to play. You roll a fair die and win $6 if you roll 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 7

A correlation coefficient is r = 0.02. How would you describe the correlation?

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

Question 8

X is normally distributed with mean 136 and standard deviation 4. Find P(X < 135.9) to 3 decimal places.

Answer 

Question 9

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 10

A trial succeeds with probability 0.3. It is repeated 5 times independently. What is the probability of exactly 2 successes? Round to 3 decimal places.

Answer 

Question 11

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

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

Question 12

For a sample of teenagers, sleep per week s (hours) and daily screen time x (hours) give s = 60 − 2.6x. What does −2.6 tell you?

• A. Each extra hour of screen time goes with about 2.6 fewer hours of sleep per week, on average
• B. Screen time causes 2.6 hours less sleep
• C. The correlation coefficient is −2.6
• D. A teenager with no screen time sleeps 2.6 hours

Question 13

For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 34 + 1.5x. Predict the score for 5 hours of revision.

Answer 

Question 14

The regression line is ŷ = 4x + 1. By how much does the predicted y change when x increases by 1?

Answer 

Question 15

Battery life is normally distributed with mean 283 minutes and standard deviation 15 minutes. Find the probability that a battery lasts between 278 and 295 minutes, to 3 decimal places.

Answer 

Question 16

A charity game costs 4 to play. The chance of winning is 0.25 and the prize is 18 (the stake is kept). Is the game fair?

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