Praxis Mathematics 5165 Domain 4: Statistics and Probability

A set of data is normally distributed with a mean of 50 and a standard deviation of 5. What percentage of the data falls between 45 and 55?

If the probability of an event A is 0.2 and the probability of an event B is 0.5, what is the probability of either A or B occurring, assuming the two events are independent?

What is the variance of the data set \( \{4, 8, 12, 16, 20\} \)?

In a binomial experiment with 10 trials and a probability of success of 0.6, what is the probability of exactly 6 successes?

If a continuous random variable X has a uniform distribution on the interval [0, 4], what is the probability that \( X \leq 2 \)?

For a set of data, if the quartile deviation is 5, what is the interquartile range?

If the correlation coefficient between two variables is 0.8, what is the coefficient of determination?

In a probability distribution, the probabilities of 5 mutually exclusive events are 0.1, 0.2, 0.3, 0.2, and 0.2. What is the entropy of this distribution?

A standard normal distribution has a mean of 0 and a standard deviation of 1. What is the z-score for a value of 2.5 in this distribution?

In a regression analysis, if the slope of the regression line is negative, what does this indicate about the relationship between the independent and dependent variables?

A test has a reliability coefficient of 0.9. If the true score is 80, what is the expected range of observed scores for this test?

In a Poisson distribution with a mean of 4, what is the probability of observing exactly 3 events?

Given a dataset with a positively skewed distribution, which of the following is true regarding its mean, median, and mode?

A box contains 3 red balls and 2 green balls. If two balls are drawn at random without replacement, what is the probability that both balls are red?

In a normal distribution, what percentage of the data lies within two standard deviations above the mean?

If a set of data has a Pearson correlation coefficient close to 0, what does this indicate about the relationship between the two variables?

What is the probability of drawing an ace from a standard deck of 52 cards, then drawing a king, assuming the ace is not replaced?

What is the expected value of a discrete random variable with the probability distribution \( P(X=1) = 0.2 \), \( P(X=2) = 0.3 \), \( P(X=3) = 0.4 \), and \( P(X=4) = 0.1 \)?

In a hypothesis test, if the p-value is less than the significance level, what is the appropriate conclusion?

A fair die is rolled twice. What is the probability that the sum of the two rolls is 8?