Find the z value to the left of the mean so that a. 98.87%...

Find the z value to the left of the mean so that
a. 98.87% of the area under the distribution curve lies to the right of it.
b. 82.12% of the area under the distribution curve lies to the right of it.
c. 60.64% of the area under the distribution curve lies to the right of it.

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Key Concepts

Standard Normal Distribution

This is a probability distribution with a mean of 0 and a standard deviation of 1. It serves as a reference for many statistical calculations and analyses, particularly in hypothesis testing and confidence interval estimation, due to its well-defined symmetrical bell curve.

Z-Score

A z-score, also known as the standard score, indicates how many standard deviations an element is from the mean. It is used to standardize individual data points from different normal distributions so that probabilities can be compared and calculated using the standard normal distribution.

Cumulative Distribution Function (CDF)

The CDF gives the probability that a random variable from a given distribution will have a value less than or equal to a particular z-score. In the context of the standard normal distribution, it is an essential tool for determining the area under the curve to the left of a specific z-score.

Percentiles and Critical Values

Percentiles represent thresholds below which a certain percentage of the data fall. Finding the z value corresponding to a given percentage involves inverse lookup of the CDF, which is a common technique in determining critical values and cutoff points in statistical analyses.

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