12th grade statistics and probability

Example

A game pays 9 points with probability 0.5, 8 points with probability 0.3, 5 points with probability 0.2. What is the expected number of points?

1. 9 × 0.5 + 8 × 0.3 + 5 × 0.2 = 7.9

Answer: 7.9

Example

A trial succeeds with probability 0.4. It is repeated 6 times independently. What is the probability of exactly 5 successes? Round to 3 decimal places.

1. 6 × 0.4^5 × 0.6^1
2. ≈ 0.037

Answer: 0.037

Example

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

1. r = 0.02: no linear correlation.

Answer: no linear correlation

Example

X is normally distributed with mean 153 and standard deviation 20. Find P(X < 134.8) to 3 decimal places.

1. z = (134.8 − 153)/20 ≈ −0.91
2. P ≈ 0.181

Answer: 0.181

Example

A team of 4 is chosen at random from 7 girls and 5 boys. Find the probability that the team is all girls, as a fraction in simplest form.

1. 7C4 / 12C4 = 35/495
2. = 7/99

Answer: 7/99

Example

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

1. 2/6 × 6 − 1 = 1

Answer: 1

Example

For students who revised 1 to 15 hours, the regression line for test score y on revision hours x is y = 22 + 7x. Predict the score for 10 hours of revision.

1. 22 + 7 × 10 = 92

Answer: 92

Example

A data set has correlation coefficient r = −0.95. How would you describe the correlation?

1. Strong negative

Answer: Strong negative