Question

use the standard normal distribution to find p(-2.25 < z < 0). click here to view page 1 of the standard normal table. click here to view page 2 of the standard normal table. a. 0.4878 b. 0.5122 c. 0.6831 d. 0.0122

Explanation:

Step1: Recall properties of standard - normal distribution

The standard - normal distribution has a mean of 0 and a standard deviation of 1. The total area under the curve is 1. Also, the distribution is symmetric about \(z = 0\). We know that \(P(Z\lt0)=0.5\) and we can use the standard - normal table to find \(P(Z\lt - 2.25)\).

Step2: Look up values in the standard - normal table

From the standard - normal table, \(P(Z\lt - 2.25)\) corresponds to the area to the left of \(z=-2.25\). Looking up the value in the table, we find that \(P(Z\lt - 2.25)=0.0122\).

Step3: Calculate \(P(-2.25\lt Z\lt0)\)

We use the formula \(P(-2.25\lt Z\lt0)=P(Z\lt0)-P(Z\lt - 2.25)\). Since \(P(Z\lt0) = 0.5\) and \(P(Z\lt - 2.25)=0.0122\), then \(P(-2.25\lt Z\lt0)=0.5 - 0.0122=0.4878\).

Answer:

A. 0.4878