Question

given a standardized normal distribution, what is the probability that z is greater than 1.64?
0.0329
0.9671
0.9329
0.0505

Explanation:

Step1: Recall the properties of the standard normal distribution

The total area under the standard normal curve is \(1\). We know that \(P(Z\leq z)\) can be found using the standard normal table (z - table). For \(z = 1.64\), from the standard normal table, \(P(Z\leq1.64)=0.9495\).

Step2: Use the formula \(P(Z > z)=1 - P(Z\leq z)\)

Substitute \(z = 1.64\) into the formula. So \(P(Z>1.64)=1 - P(Z\leq1.64)\).
Since \(P(Z\leq1.64) = 0.9495\), then \(P(Z>1.64)=1- 0.9495=0.0505\).

Answer:

\(0.0505\) (the fourth option)