Find endpoint(s) on a N(0,1) density with the given...

Find endpoint(s) on a $N(0,1)$ density with the given property.
P.137 (a) The area to the left of the endpoint is about 0.10
(b) The area to the right of the endpoint is about 0.80
(c) The area between $\pm z$ is about 0.95 .

Key Concepts

Standard Normal Distribution

The standard normal distribution is a normal probability distribution with a mean of 0 and a standard deviation of 1. It is widely used in statistics as a reference distribution because of its unique properties and symmetry, and many statistical models assume data follows this distribution.

Cumulative Distribution Function (CDF)

The cumulative distribution function for a probability distribution gives the probability that a random variable will take a value less than or equal to a particular value. For the standard normal distribution, the CDF is used to determine the area under the curve to the left of a given z-score and is a fundamental tool for finding probabilities.

Quantiles and Percentiles

Quantiles (or percentiles) are points in the domain of the probability distribution that correspond to specific cumulative probabilities. In the context of the standard normal distribution, quantiles are used to find z-scores such that the corresponding tail or central area under the curve meets a given probability criterion.

Symmetry of the Normal Distribution

The normal distribution is symmetric about its mean. This symmetry implies that the area under the curve to the left of a negative z-value is equal to the area to the right of the corresponding positive z-value. This property is essential when calculating intervals and determining endpoints that enclose a specific central area of the distribution.

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