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.
( a) The area to the left of the endpoint is about 0.70
(b) The area to the right of the endpoint is about $0.01 .$
(c) The area between $\pm z$ is about 0.90 .

Key Concepts

Standard Normal Distribution

The standard normal distribution is a continuous probability distribution with a mean of 0 and a standard deviation of 1. This distribution is symmetric about zero and is extensively used in statistics for hypothesis testing, confidence interval construction, and many other inference techniques. Its probability density function (PDF) forms the familiar bell-shaped curve.

Cumulative Distribution Function (CDF)

The cumulative distribution function represents the probability that a random variable drawn from a distribution is less than or equal to a particular value. In the context of the standard normal distribution, the CDF is used to find the probability or area associated with specific endpoints or z-scores.

Inverse Cumulative Distribution Function (Quantile Function)

The inverse cumulative distribution function, or quantile function, is used to determine the z-score associated with a given cumulative probability. By applying this function, one can find specific endpoints or critical values that correspond to particular areas or tail probabilities within the normal distribution.

Symmetry in the Normal Distribution

The symmetry of the standard normal distribution about its mean (zero) is a key concept that allows for the determination of endpoints around the center. This property implies that probabilities on equivalent distances from the mean are equal, which simplifies the process of finding central intervals and symmetric tail probabilities.

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