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: Use the standard normal distribution property

The total area under the standard normal curve is \(1\). The cumulative - distribution function of the standard normal distribution is denoted as \(\varPhi(z)=P(Z\leq z)\). We want to find \(P(Z > 1.64)\).
By the property \(P(Z>z)=1 - P(Z\leq z)\).

Step2: Look up the value in the standard normal table

Looking up the value of \(z = 1.64\) in the standard normal table (z - table). The standard normal table gives the value of \(\varPhi(1.64)\).
From the standard normal table, \(\varPhi(1.64)=0.9495\) (the value in the table is for \(P(Z\leq1.64)\)).

Step3: Calculate \(P(Z > 1.64)\)

Using the formula \(P(Z>1.64)=1-\varPhi(1.64)\).
Substitute \(\varPhi(1.64) = 0.9495\) into the formula: \(P(Z>1.64)=1 - 0.9495=0.0505\)

Answer:

\(0.0505\)