Question

-0.22 < z < 1.9

Explanation:

Step1: Use the standard normal distribution table

The area to the left of \(z = 1.9\) is \(P(Z<1.9)\). From the standard - normal table, \(P(Z < 1.9)=0.9713\).

Step2: Find the area to the left of \(z=-0.22\)

The area to the left of \(z=-0.22\) is \(P(Z < - 0.22)\). From the standard - normal table, \(P(Z<-0.22)=0.4129\).

Step3: Calculate the required probability

We want to find \(P(-0.22 < Z < 1.9)\). Using the formula \(P(a < Z < b)=P(Z < b)-P(Z < a)\), we substitute \(a=-0.22\) and \(b = 1.9\). So \(P(-0.22<Z<1.9)=P(Z < 1.9)-P(Z < - 0.22)\).
Substitute the values: \(P(-0.22 < Z < 1.9)=0.9713-0.4129\).

Answer:

\(0.5584\)