Lecture 3: Probability and Normal Distribution Review

30 vocabulary flashcards generated from the lecture on probability and normal distribution, covering exam information, R functions (PNorm, QNorm), the 68-95-99.7 rule, and key statistical terms.

Normal Distribution

A common probability distribution, often bell-shaped and symmetrical, described by its mean and standard deviation.

Approximately Normally Distributed

A key phrase in problems indicating that data follows a normal distribution, allowing the use of specific statistical methods.

Mean (μ)

The average or central value of a dataset in a normal distribution.

Standard Deviation (σ)

A measure of the dispersion or spread of data points around the mean in a normal distribution.

Quality Control Test

A process to check if a product (e.g., ketchup bottle) falls within specified acceptable limits; exceeding or falling below limits results in failure.

Z-value (Z-score)

A standardized value that indicates how many standard deviations an element is from the mean; calculated as (X - μ) / σ.

PNorm Function (R)

An R function used to calculate the cumulative probability (area to the left) for a given value in a normal distribution.

PNorm Probability Direction

PNorm always calculates the probability that a value is less than or equal to the specified input (area to the left of the value).

Exact Probability (with PNorm)

Achieved by plugging the actual value, mean, and standard deviation into PNorm, rather than using a rounded Z-value.

Probability Between Two Values

Calculated by finding the PNorm of the upper value and subtracting the PNorm of the lower value (PNorm(upper) - PNorm(lower)).

Probability Greater Than a Value

Calculated by subtracting the PNorm of the value from 1 (1 - PNorm(value)), as PNorm gives the probability to the left.

QNorm Function (R)

An R function used to find the value (cutoff) corresponding to a given cumulative probability (percentile) in a normal distribution.

Cutoff Question

A type of question that asks for a specific value (e.g., temperature, score) that separates a given percentage of data, requiring the use of QNorm.

QNorm Probability Direction

QNorm requires the input probability to be the cumulative probability to the left of the desired cutoff value.

68-95-99.7 Rule

A rule stating that for a nearly normal distribution, about 68% of data falls within 1 standard deviation, 95% within 2, and 99.7% within 3 standard deviations of the mean.

One Standard Deviation (68% Rule)

Approximately 68% of data in a normal distribution lies within one standard deviation above and below the mean (μ ± 1σ).

Two Standard Deviations (95% Rule)

Approximately 95% of data in a normal distribution lies within two standard deviations above and below the mean (μ ± 2σ).

Three Standard Deviations (99.7% Rule)

Approximately 99.7% of data in a normal distribution lies within three standard deviations above and below the mean (μ ± 3σ).

Rare Occurrences (Normal Distribution)

Data points falling four or more standard deviations away from the mean in a nearly normal distribution, which are highly infrequent.

Independent Events (Homework)

Events where the outcome of one does not affect the outcome of another; their combined probability is found by multiplying individual probabilities.

General Addition Rule (Homework)

Formula for finding the probability of A or B: P(A or B) = P(A) + P(B) - P(A and B).

Time Unit Conversion

The process of converting time from hours and minutes into a single unit (e.g., total minutes) for accurate statistical calculations.