Statistics: Normal Distribution Concepts

<p>683 (D)</p> Signup and view all the answers

<p>To express original scores in units of standard deviation (A)</p> Signup and view all the answers

<p>0 (C)</p> Signup and view all the answers

<p>Z scores can be interpreted as the number of standard deviations an individual score is from the mean. (D)</p> Signup and view all the answers

<p>14.14 (D)</p> Signup and view all the answers

<p>0.000 (A)</p> Signup and view all the answers

<p>They are transformed to a different scale with a mean of 0 and standard deviation of 1. (B)</p> Signup and view all the answers

<p>It is a symmetrical distribution. (D)</p> Signup and view all the answers

<p>It provides a theoretical model for describing distributions. (B)</p> Signup and view all the answers

<p>It can represent skewed data. (D)</p> Signup and view all the answers

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

<p>As a perfectly smooth frequency polygon. (B)</p> Signup and view all the answers

<p>Range. (C)</p> Signup and view all the answers

<p>It can take on any value within a given range. (B)</p> Signup and view all the answers

<p>Descriptive statistics that summarize data. (A)</p> Signup and view all the answers

<p>The point below which a specific percentage of cases fall. (A)</p> Signup and view all the answers

<p>Subtract 50% from 98.5%. (B)</p> Signup and view all the answers

<p>2.17 (C)</p> Signup and view all the answers

<p>Add the areas between each score and the mean. (A)</p> Signup and view all the answers

<p>36.25% (D)</p> Signup and view all the answers

<p>Subtract the smaller area from the larger area. (B)</p> Signup and view all the answers

<p>11.09% of the total population falls between these scores. (C)</p> Signup and view all the answers

<p>The point where half of the data is below and half is above. (B)</p> Signup and view all the answers

<p>The difference between the raw score and the mean, divided by the standard deviation. (D)</p> Signup and view all the answers

<p>0.5000 (D)</p> Signup and view all the answers

<p>Nominal and ordinal variables (D)</p> Signup and view all the answers

<p>1.00 (B)</p> Signup and view all the answers

<p>Probabilities represent an area under the curve. (D)</p> Signup and view all the answers

<p>For a range of values under the curve (D)</p> Signup and view all the answers

<p>All outcomes have equal probabilities (C)</p> Signup and view all the answers

<p>0.3334 (C)</p> Signup and view all the answers

<p>Continuous distributions (C)</p> Signup and view all the answers

<p>0.0987 (C)</p> Signup and view all the answers

<p>0.8749 (C)</p> Signup and view all the answers

<p>88 (A)</p> Signup and view all the answers

<p>The probability of selecting them is less than 0.0026. (A)</p> Signup and view all the answers

<p>Probability decreases with distance from the mean. (A)</p> Signup and view all the answers

<p>The probability distribution of continuous variables. (A)</p> Signup and view all the answers

<p>0.6826 (B)</p> Signup and view all the answers

<p>Close scores have a higher selection probability. (B)</p> Signup and view all the answers

<p>2.6 (D)</p> Signup and view all the answers

<p>It indicates the relationship between a score and the mean. (B)</p> Signup and view all the answers

<p>1.00 (B)</p> Signup and view all the answers

<p>0.0192 (A)</p> Signup and view all the answers

<p>192 (A)</p> Signup and view all the answers

<p>80.23% (C)</p> Signup and view all the answers

<p>8.85% (B)</p> Signup and view all the answers

<p>It is unlikely to draw that card. (A)</p> Signup and view all the answers

<p>The raw score is below the mean. (D)</p> Signup and view all the answers

<p>The number of successes and events (A)</p> Signup and view all the answers

<p>There are 52 other cards in the deck. (C)</p> Signup and view all the answers

<p>63.68% (C)</p> Signup and view all the answers

<p>65.54% (C)</p> Signup and view all the answers

<p>They will maintain a certain proportional relationship. (C)</p> Signup and view all the answers

<p>95.44% (A)</p> Signup and view all the answers

<p>110 (D)</p> Signup and view all the answers

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

<p>1.96 (A)</p> Signup and view all the answers

<p>950 (D)</p> Signup and view all the answers

<p>Subtract 50% from the percentile (C)</p> Signup and view all the answers

<p>Add the areas between each score and the mean (C)</p> Signup and view all the answers

<p>121.70 (D)</p> Signup and view all the answers

<p>0.4850 (D)</p> Signup and view all the answers

<p>The sum of the individual areas from the mean to each score (A)</p> Signup and view all the answers

<p>11.09% (C)</p> Signup and view all the answers

<p>Percentiles indicate the positions of scores in relation to the total cases. (A)</p> Signup and view all the answers

<p>Combine the individual areas from the mean (B)</p> Signup and view all the answers

Standard scores that represent the number of standard deviations a data point is from the mean of a normal distribution.

A measure of the amount of variation or dispersion of a set of values.

A bell-shaped probability distribution where most data values cluster around the mean.

The proportion of data points within a specific range of values (expressed as percentage).

A distance from the mean that contains 68.26% of the area under the curve in a normal distribution.

A theoretical model in statistics that describes a specific frequency distribution. It's perfectly smooth, unimodal (one peak), and symmetrical.

A distribution with a single peak, maximum or mode.

A distribution where both sides mirror each other. Left and right sides are the same.

An idealized representation of a concept; not an exact replication of real-world observations.

A distribution made from real-world observations or data, not theory.

An arrangement of data that indicates how often various values occur in a data set.

Summary measures used to describe data characteristics (e.g., measures of central tendency, dispersion).

Statistics that represent the typical or average value in a dataset (mean, median, mode).

A method to transform raw scores into standardized scores (Z-scores) with a mean of 0 and a standard deviation of 1.

The formula used to calculate Z scores. It involves subtracting the mean from the individual score and then dividing by the standard deviation.

A normal distribution with a mean of 0 and a standard deviation of 1.

An original data point or measurement in its actual units.

A table or graph that shows the probability of each possible outcome of an event.

A probability distribution where the variable can only take on specific, separate values.

A probability distribution where the variable can take on any value within a range.

Probabilities are calculated for ranges of values under the normal curve, rather than for specific values.

A variable that can only take on whole numbers, such as the number of siblings you have.

A variable that can take on any value within a range, like the height of a person.

Calculating probability for discrete variables involves finding the likelihood of specific events. For continuous variables, probabilities are calculated for ranges of values.

A percentile represents the percentage of scores that fall below a certain value. For example, the 70th percentile means that 70% of the scores are below that value.

To find a raw score from a percentile, we first convert the percentile to a proportion, then find the corresponding Z-score using a Z-table. Finally, use the Z-score formula to calculate the raw score.

The area between two scores on the same side of the mean is calculated by finding the area between each score and the mean, and subtracting the smaller area from the larger one.

To find the area between two scores on opposite sides of the mean, add the areas between each score and the mean.

Understanding the area under the normal curve allows us to estimate probabilities of certain events happening.

Using the Z-score formula, we find the Z-scores for 93 and 112. Then, using a Z-table, we find the area between each Z-score and the mean, and add them to find the total area between 93 and 112.

We calculate the Z-scores for 113 and 121 using the Z-score formula, then find the areas between each Z-score and the mean. Subtract the smaller area from the larger area to find the total area between 113 and 121.

We can use the normal curve to estimate probabilities of different scores occurring in a given population. For example, we can find the probability of a randomly selected individual having an IQ score above 120.

The chance of randomly selecting a data point within a specific range of values in a continuous distribution (like a normal curve).

Transforming a raw score (like an IQ score) into a standardized Z-score to compare it to a standard normal distribution.

The chance of selecting a value greater or less than the mean in a continuous distribution.

The theoretical concept of repeating an experiment or measurement an infinite number of times to approach the true probability.

The tendency for most data points in a normal distribution to cluster around the mean.

A standard deviation from the mean defines a specific range within a normal distribution and carries a known probability.

The chance of selecting a data point very far from the mean, beyond multiple standard deviations.

The area under a normal curve representing a specific range of values corresponds to the probability of selecting a data point within that range.

A table that provides probabilities for the standard normal distribution, based on Z-scores.

Understanding that probabilities in a continuous distribution represent the likelihood of selecting a certain value or range of values over many trials.

A Z-score represents how many standard deviations a data point is away from the mean of a distribution. It standardizes scores to the theoretical normal curve.

The area under a normal curve represents the proportion of data points within a specific range of values. This area directly corresponds to the probability of finding a data point in that range.

The area within one standard deviation from the mean encompasses approximately 68.26% of the total area under the curve.

Z-scores allow us to compare data points from different distributions, regardless of their original units. They make it possible to compare apples and oranges!

Standardized scores (Z-scores) simplify data analysis and comparison. They allow us to easily understand how a score relates to the overall distribution regardless of the original units, making it easier to draw comparisons and analyze the data.

A Z score represents a specific point on the normal curve. The area under the curve between that point and the mean represents the proportion of data points between the score and the mean.

A positive Z score indicates a value above the mean, while a negative Z score indicates a value below the mean.

To find the area below a positive Z score, add the area between the score and the mean to 50%. To find the area below a negative Z score, use the 'Area Beyond Z' value in the Z table.

To find the area above a positive Z score, use the 'Area Beyond Z' value in the Z table.

To find the raw score, convert the percentile to a proportion, look up the corresponding Z-score in a table, and use the Z-score formula with the mean and standard deviation to calculate the raw score.

To find the area between scores on opposite sides of the mean, add the areas between each score and the mean.

To find the area between scores on the same side of the mean, subtract the smaller area (closer to the mean) from the larger area.

Using the area under the normal curve, we can approximate the chance of a specific data point occurring in a given population. For example, the probability of a randomly selected adult having an IQ score above 130.

The formula for calculating probability is:

Probability (event) = Number of successful events / Total number of events

Probabilities range from 0.00 (impossible) to 1.00 (certain). The higher the probability, the more likely the event is to occur.

The normal curve can be used to estimate the probability of a randomly selected value falling within a certain range.

The probability of drawing the King of Hearts from a deck of cards is 1/52 (or approximately 0.0192).

We can estimate the probability of a specific value or range of values by looking at the area under the normal curve corresponding to that value or range.

A high probability indicates that an event is very likely to occur. A probability close to 1.00 means the event is almost certain.

A low probability indicates that an event is unlikely to occur. A probability close to 0.00 means the event is highly improbable.