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### How to Find Percentiles for a *t*-Distribution

When you want to find percentiles for a *t*-distribution, you can use the *t*-table. A *percentile* is a number on a statistical distribution whose less-than probability is the given percentage; for example, [more…]

### How to Find *t**-Values for Confidence Intervals

*Confidence intervals* estimate population parameters, such as the population mean, by using a statistic (for example, the sample mean) plus or minus a margin of error. To compute the margin of error for [more…]

### How to Identify a Sampling Distribution

In statistics, a sampling distribution is based on sample averages rather than individual outcomes. This makes it different from a distribution. Here’s why: A [more…]

### How Sample Size Affects Standard Error

The size (*n*) of a statistical sample affects the standard error for that sample. Because *n* is in the denominator of the standard error formula, the standard error decreases as [more…]

### How Population Standard Deviation Affects Standard Error

In statistics, the standard deviation in a population affects the standard error for that population. Standard deviation measures the amount of variation in a population. In the standard error formula [more…]

### How a Normal Distribution Affects the Shape of a Sampling Distribution

In statistics, when the original distribution for a population *X* is normal, then you can also assume that the shape of the sampling distribution, or [more…]

### How a Sampling Distribution Is Affected When the Distribution Is Not Normal

In statistics, if a population *X* has any distribution that is *not* normal, or if its distribution is unknown, you can’t automatically say the distribution of the sample means [more…]

### How to Find the Sampling Distribution of a Sample Proportion

If you use a large enough statistical sample size, you can apply the Central Limit Theorem (CLT) to a sample proportion for categorical data to find its sampling distribution. The [more…]

### How to Find Probabilities for a Sample Proportion

You can find probabilities for a sample proportion by using the normal approximation as long as certain conditions are met. For example, say that a statistical study claims that 0.38 or 38% of all the [more…]

### How to Define a Random Statistical Variable

In statistics, a *random variable* is a characteristic, measurement, or count that changes randomly according to a certain set or pattern. Random variables are usually denoted with capital letters such as [more…]

### Statistics: Discrete and Continuous Random Variables

In statistics, numerical random variables represent counts and measurements. They come in two different flavors: discrete and continuous, depending on the type of outcomes that are possible: [more…]

### How to Find Right-Tail Values and Confidence Intervals Using the *t*-Table

You can use a *t*-table to find right-tail probabilities and *p*-values for hypothesis tests and to find *t**-values (critical values) for a confidence interval involving [more…]

### How to Identify the Notation for the Mean and Variance of a Discrete Random Variable

Two of the most important terms in statistics are mean and variance, and so you need to be able to identify their notations when working with discrete random variables. [more…]

### How to Identify a Random Binomial Variable

The most well-known and loved discrete random variable in statistics is the binomial. *Binomial* means *two names*and is associated with situations involving two outcomes; for example yes/no, or success/failure [more…]

### How to Find the Mean, Variance, and Standard Deviation of a Binomial Distribution

Because the binomial distribution is so commonly used, statisticians went ahead and did all the grunt work to figure out nice, easy formulas for finding its mean, variance, and standard deviation. The [more…]

### Understanding the Statistical Properties of the Normal Distribution

When you understand the properties of the normal distribution, you'll find it easier to interpret statistical data. A continuous random variable *X* has a normal distribution if its values fall into a smooth [more…]

### Using the *Z*-Distribution to Find the Standard Deviation in a Statistical Sample

One very special member of the normal distribution family is called the standard normal distribution, or *Z*-distribution. In statistics, the *Z-distribution* [more…]

### How to Change an *X*-Value to a *Z*-Value

If you have a statistical sample with a normal distribution, you can plug an *x*-value for this distribution into a special equation to find its *z*-value. The [more…]

### How to Find Probabilities for *Z* with the *Z*-Table

You can use the *Z*-table to find a full set of "less-than" probabilities for a wide range of *z*-values. To use the *Z-*table to find probabilities for a statistical sample with a standard normal [more…]

### How to Find Statistical Probabilities in a Normal Distribution

If your statistical sample has a normal distribution (*X*), then you can use the *Z*-table to find the probability that something will occur within a defined set of parameters. For example, you could look [more…]

### How to Find a Percentile for a Normal Distribution

A popular normal distribution problem involves finding percentiles for *X*. That is, you are given the percentage or statistical probability of being at or below a certain [more…]

### How to Tell a *Z*-Distribution from a *t*-Distribution

Although the normal (*Z*-) distribution and *t*-distribution are similar, they look different from each other and are used for different statistical purposes. The normal distribution is that well-known bell-shaped [more…]

### How to Indicate Possible Outcomes for a Discrete Random Variable

A discrete random variable *X* can take on a certain set of possible outcomes, and each of those outcomes has a certain statistical probability of occurring. The notation used for any specific outcome is [more…]

### How to Find Probabilities for a Sample Mean

In statistics, you can easily find probabilities for a sample mean if it has a normal distribution. Even if it doesn’t have a normal distribution, or the distribution is not known, you can find probabilities [more…]

### How to Find Binomial Probabilities Using a Statistical Formula

After you identify that a random variable *X* has a binomial distribution, you'll likely want to find probabilities for *X.* The good news is that you don't have to find them from scratch; you get to use established [more…]