Probability and Normal Distribution

<p>They are rare and lie far from the mean (A)</p> Signup and view all the answers

<p>0.5 to the right and 0.5 to the left (A)</p> Signup and view all the answers

<p>A bell-shaped curve (C)</p> Signup and view all the answers

<p>It determines the location of the distribution (C)</p> Signup and view all the answers

<p>Distributions will have different spread but the same central peak (A)</p> Signup and view all the answers

<p>The value is above the mean. (C)</p> Signup and view all the answers

<p>$z = \frac{x - \mu}{\sigma}$ (C)</p> Signup and view all the answers

<p>It maintains the same shape of the distribution. (D)</p> Signup and view all the answers

<p>To compare different x-values on the same scale. (A)</p> Signup and view all the answers

<p>The distance from the mean in standard deviation units. (B)</p> Signup and view all the answers

<p>Standardizing values to z-scores. (A)</p> Signup and view all the answers

<p>The value is equal to the mean. (B)</p> Signup and view all the answers

<p>Z-scores provide a way to identify positions in a distribution. (C)</p> Signup and view all the answers

<p>The number of standard deviations a value is from the mean (A)</p> Signup and view all the answers

<p>82 (A)</p> Signup and view all the answers

<p>95% (B)</p> Signup and view all the answers

<p>It would be considered one of the highest marks (D)</p> Signup and view all the answers

<p>The score falls below the mean by 2 standard deviations (C)</p> Signup and view all the answers

<p>The Z-score is 0 (A)</p> Signup and view all the answers

<p>Total area under the curve is always less than 1 (D)</p> Signup and view all the answers

<p>Most scores are concentrated around the mean (D)</p> Signup and view all the answers

A specific normal distribution with a mean of 0 and a standard deviation of 1, used to standardize other normal distributions for easier comparisons.

Converting raw data (x-values) into z-scores to compare values on a common scale, regardless of the original data's mean and standard deviation.

A value representing the location of a data point in a standardized normal distribution, calculated by how many standard deviations it is away from the mean.

z = (x - μ) / σ

An individual data point in a raw data set.

The average value of a data set.

A measure of the spread or variability of data around the mean.

The shape of the distribution doesn't change when converting to z-scores, only the scale of measurement changes.

A symmetrical bell-shaped curve where data points cluster around the mean, median, and mode, tapering off towards the extremes.

In a normal distribution, the arithmetic average, middle value, and most frequent value are all equal and located at the center of the distribution.

The total area under the normal distribution curve equals 1.00.

The normal distribution is symmetrical around the mean. The left and right halves are mirror images.

The position of the normal distribution curve is determined by its mean (μ).

The spread of data, also called dispersion, is measured by the standard deviation (σ).

A measure of how much the data varies from the mean in a normal distribution.

Extreme values (very large or very small) are very rare in a normal distribution.

The standard deviation (σ) significantly affects how a single data point's position within a data set is interpreted. Data with a larger standard deviation shows more variation and a wider dispersion of values compared to a smaller standard deviation.

A single data point without context (like its standard deviation and mean) doesn't indicate if it's 'good' or 'bad'—it's only meaningful relative to the data set it comes from.

A rule that describes the typical distribution of data in a normal (bell-shaped) distribution. It states that approximately 68%, 95%, and 99.7% of the data fall within one, two, and three standard deviations of the mean, respectively.

Approximately 68% of the data in a normal distribution falls within one standard deviation of the mean.

Approximately 95% of the data in a normal distribution falls within two standard deviations of the mean.

Approximately 99.7% of the data in a normal distribution falls within three standard deviations of the mean.

The normal distribution is a common probability distribution widely applicable across various fields—from business to everyday life.

A data point's position is relative to the mean and standard deviation of its distribution.