standard normal distribution

(noun)

The normal distribution with a mean of zero and a standard deviation of one.

Related Terms

Examples of standard normal distribution in the following topics:

  • The Standard Normal Distribution

    • The standard normal distribution is a normal distribution of standardized values called z-scores.
    • For example, if the mean of a normal distribution is 5 and the standard deviation is 2, the value 11 is 3 standard deviations above (or to the right of) the mean.
    • The mean for the standard normal distribution is 0 and the standard deviation is 1.
    • The transformation z = (x − µ)/σ produces the distribution Z ∼ N ( 0,1 ) .
    • The value x comes from a normal distribution with mean µ and standard deviation σ.

  • Student Learning Outcomes

  • Standard Normal Distribution

    • State the mean and standard deviation of the standard normal distribution
    • A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.
    • Areas of the normal distribution are often represented by tables of the standard normal distribution.
    • A portion of a table of the standard normal distribution is shown in Table 1.
    • A portion of a table of the standard normal distribution

  • Chi Square Distribution

    • A standard normal deviate is a random sample from the standard normal distribution.
    • The Chi Square distribution is the distribution of the sum of squared standard normal deviates.
    • The degrees of freedom of the distribution is equal to the number of standard normal deviates being summed.
    • The area of a Chi Square distribution below 4 is the same as the area of a standard normal distribution below 2, since 4 is 22.
    • Consider the following problem: you sample two scores from a standard normal distribution, square each score, and sum the squares.

  • Normal distribution model

    • Specifically, the normal distribution model can be adjusted using two parameters: mean and standard deviation.
    • Figure 3.2 shows the normal distribution with mean 0 and standard deviation 1 in the left panel and the normal distributions with mean 19 and standard deviation 4 in the right panel.
    • If a normal distribution has mean µ and standard deviation σ, we may write the distribution as N(µ,σ).
    • Write down the short-hand for a normal distribution with (a) mean 5 and standard deviation 3, (b) mean -100 and standard deviation 10, and (c) mean 2 and standard deviation 9.
    • The normal distribution with mean 0 and standard deviation 1 is called the standard normal distribution.

  • Areas Under Normal Distributions

    • State the proportion of a normal distribution within 1 standard deviation of the mean
    • State the proportion of a normal distribution that is more than 1.96 standard deviations from the mean
    • Figure 1 shows a normal distribution with a mean of 50 and a standard deviation of 10.
    • Figure 2 shows a normal distribution with a mean of 100 and a standard deviation of 20.
    • Figure 3 shows a normal distribution with a mean of 75 and a standard deviation of 10.

  • Change of Scale

    • In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary.
    • In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary.
    • In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution.
    • The use of "$Z$" is because the normal distribution is also known as the "$Z$ distribution".
    • They are most frequently used to compare a sample to a standard normal deviate (standard normal distribution, with $\mu = 0$ and $\sigma = 1$).

  • The Normal Distribution

    • Normal distributions are a family of distributions all having the same general shape.
    • If $\mu = 0$ and $\sigma = 1$, the distribution is called the standard normal distribution or the unit normal distribution, and a random variable with that distribution is a standard normal deviate.
    • The simplest case of normal distribution, known as the Standard Normal Distribution, has expected value zero and variance one.
    • The normal distribution carries with it assumptions and can be completely specified by two parameters: the mean and the standard deviation.
    • The empirical rule is a handy quick estimate of the spread of the data given the mean and standard deviation of a data set that follows normal distribution.

  • Introduction to Normal Distributions

    • Normal distributions can differ in their means and in their standard deviations.
    • The parameters μ and σ are the mean and standard deviation, respectively, and define the normal distribution.
    • Normal distributions are defined by two parameters, the mean (μ) and the standard deviation (σ).
    • 68% of the area of a normal distribution is within one standard deviation of the mean.
    • Approximately 95% of the area of a normal distribution is within two standard deviations of the mean.

  • Introduction

    • The normal, a continuous distribution, is the most important of all the distributions.
    • Some of your instructors may use the normal distribution to help determine your grade.
    • Most IQ scores are normally distributed.
    • Often real estate prices fit a normal distribution.
    • In this chapter, you will study the normal distribution, the standard normal, and applications associated with them.