Question

question 2
given a standardized normal distribution, what is the probability that z is between 1.57 and 1.84?
0.9089
0.9189
0.0253

Explanation:

Step1: Find the cumulative probabilities

Using the standard normal distribution table (or Z - table), find \(P(Z < 1.84)\) and \(P(Z < 1.57)\).
From the Z - table, \(P(Z < 1.84)=0.9671\) and \(P(Z < 1.57) = 0.9418\).

Step2: Calculate the probability between two Z - values

The formula for \(P(a<Z < b)\) is \(P(Z < b)-P(Z < a)\).
Here, \(a = 1.57\) and \(b = 1.84\), so \(P(1.57<Z < 1.84)=P(Z < 1.84)-P(Z < 1.57)\).
Substitute the values: \(P(1.57 < Z < 1.84)=0.9671 - 0.9418\).
\(0.9671-0.9418 = 0.0253\)

Answer:

\(0.0253\)