IM3 Stats Review

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Front

How do you calculate the probability of an event?

Back

Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What does it mean for data to be normally distributed?

Back

It means that the data follows a bell-shaped curve where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

Front

What is the mean in a data set?

Back

The mean is the average of a set of numbers, calculated by adding all the values together and dividing by the number of values.

Front

What is the standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

Front

How do you find the z-score of a value?

Back

The z-score is calculated by subtracting the mean from the value and then dividing by the standard deviation: z = (X - μ) / σ.

Front

What is the probability of rolling an even number on a six-sided die?

Back

The probability of rolling an even number (2, 4, or 6) is 3/6 or 1/2.

Front

What is the probability of drawing two green marbles from a bag without replacement?

Back

If there are 6 green marbles in a bag of 17, the probability of drawing one green marble and then another is (6/17) * (5/16) = 30/272 = 15/136.

Front

What is the significance of the 95% confidence interval?

Back

A 95% confidence interval means that if you were to take 100 different samples and compute a confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true population mean.