Question

find the indicated probability. use the standard normal distribution to find p(-2.25 < z < 0). 0.6831 0.5122 0.4878 0.0122

Explanation:

Step1: Recall property of standard - normal distribution

The standard - normal distribution is symmetric about \(z = 0\). We know that \(P(Z\lt0)=0.5\) and we can use the z - table to find \(P(Z\lt - 2.25)\).

Step2: Look up value in z - table

Looking up \(z=-2.25\) in the standard - normal (z -) table, we find that \(P(Z\lt - 2.25)=0.0122\).

Step3: Calculate the probability

We want to find \(P(-2.25\lt Z\lt0)\). Using 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:

C. 0.4878