Modules 7, 8, 10, 11, 12 Practice

Front

What is the mean of a random variable?

Back

The mean of a random variable is the average value it takes, calculated as the sum of all possible values multiplied by their probabilities.

Front

Define variance in statistics.

Back

Variance is a measure of how much values in a data set differ from the mean. It is calculated as the average of the squared differences from the mean.

Front

What is the formula for calculating the toll collected from a car crossing a bridge with a variable number of passengers?

Back

The formula is: Total Toll = $3 + $0.50 * (number of passengers).

Front

How do you calculate the standard deviation from variance?

Back

The standard deviation is the square root of the variance.

Front

What does a P-value represent in hypothesis testing?

Back

A P-value indicates the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true.

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

Explain the Standard Deviation Rule (68-95-99.7 rule).

Back

This rule states that in a normal distribution: about 68% of data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

Front

What is the significance of a mean value in a data set?

Back

The mean value provides a central point around which the data is distributed, helping to summarize the data set with a single representative value.

Front

How do you interpret a P-value of 0.23 in hypothesis testing?

Back

A P-value of 0.23 suggests that there is not enough evidence to reject the null hypothesis, indicating that the observed data is not significantly different from what would be expected under the null hypothesis.

Front

What is a random variable?

Back

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.