Probability, Random Variables, and Probability Distributions

$\sum [P(X = x) / x]$

$1 / \sum [x \cdot P(X = x)]$

$\sum [x \cdot P(X = x)]$

$P(X = x) / x$

Each individual rectangle must have an area representing its statistical significance.

It can be any positive value.

It must equal to 1.

It must be greater than or equal to zero but less than one.

There are two distinct groups of values

The values are concentrated on the left side

There is a dominant group of values

The distribution is normal or bell-shaped

Median

Range

Standard deviation

Mode

Range

Standard deviation

Mean

Interquartile range (IQR)

There are two distinct groups of values

The distribution is normal or bell-shaped

The values are concentrated on the left side

The values are concentrated on the right side

No change occurs because probabilities still sum to one after normalization.

Both mean and standard deviation double since all probabilities double.

The mean doubles while there is no change in standard deviation due to it being an absolute measure of spread unaffected by changes in probability levels until they sum up to one.

The mean stays constant while the standard deviation increases as the standard deviation size decreases since relative distances between terms remain unchanged but their likelihoods are altered.

The sample size n is greater than 30.

The probability of success p is exactly 0.5.

All trials are independent, and there are only two possible outcomes.

np and n(1-p) are both greater than 10.

The number of students in a classroom

The height of a person

The number of cars passing through an intersection in a given hour

The number of heads that appear when flipping a coin three times

Both $np$ and $n(1-p)$ are greater than or equal to 10.

Both $np$ and $n(1-p)$ must be whole numbers.

Both $np$ and $n(1-p)$ are less than or equal to .5.

Both $np$ and $n(1-p)$ must equal each other.