Here are the essential concepts you must grasp in order to answer the question correctly.
Standard Normal Distribution
The standard normal distribution is a special case of the normal distribution where the mean is 0 and the standard deviation is 1. It is represented by the variable 'Z', which indicates how many standard deviations an element is from the mean. This distribution is symmetric and bell-shaped, making it essential for calculating probabilities and areas under the curve.
Recommended video:
Finding Standard Normal Probabilities using z-Table
Area Under the Curve
In statistics, the area under the curve (AUC) of a probability distribution represents the probability of a random variable falling within a certain range. For the standard normal distribution, this area can be found using Z-scores and standard normal tables or technology. The shaded region in the graph indicates the probability associated with the Z-scores between -0.9 and 0.
Recommended video:
Z-Scores from Probabilities
Z-Score
A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is calculated by subtracting the mean from the value and then dividing by the standard deviation. Z-scores are crucial for standardizing scores across different distributions, allowing for comparison and the calculation of probabilities using the standard normal distribution.
Recommended video:
Z-Scores From Given Probability - TI-84 (CE) Calculator