Statistics

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is selected at random, what is the probability that it is blue?

A basketball player makes 80% of her free throws. Assuming each attempt is independent, what is the probability that she makes exactly 3 of her next 4 free throws?

A card is drawn from a standard 52-card deck. What is the probability that the card is a heart or a king?

A class has 12 boys and 18 girls. If two students are selected at random without replacement, what is the probability that both are girls?

A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

A hypothesis test uses H₀: μ = 50 and Hₐ: μ > 50. The test produces a p-value of 0.03. At the α = 0.05 significance level, what conclusion should be made?

A poll finds that 240 out of 400 surveyed voters support a proposal. Find the sample proportion.

A population has a mean of 100 and a standard deviation of 15. For samples of size 25, find the mean and standard error of the sampling distribution of the sample mean.

A random sample of 64 students has a mean study time of 12 hours per week. The population standard deviation is known to be 4 hours. Construct a 95% confidence interval for the population mean using z* = 1.96.

A regression line is given by ŷ = 12 + 3.5x. Predict y when x = 8.