Question

suppose z has a standard normal distribution with a mean of 0 and standard deviation of 1. 27% of the possible z values are smaller than. use your z - table and give your answer to 2 decimal places.

Explanation:

Step1: Find the z - score

We know that if \(P(Z < z)=0.27\), we need to look up the value in the standard normal (z - table).
The standard normal table gives the cumulative probability \(P(Z < z)\).

Step2: Locate the value in the table

Looking at the z - table (the cumulative distribution function of the standard normal distribution \(\varPhi(z)=P(Z < z)\)), we search for the value closest to \(0.27\).
The z - table is a table of values for the standard normal distribution. For a cumulative probability of \(0.27\), the corresponding z - score.
From the standard normal table, \(z\approx - 0.61\) (by looking at the row and column values in the z - table. The cumulative probability \(0.27\) is located by first looking at the rows for the integer and first decimal part of \(z\) and then the columns for the second decimal part).

Answer:

\(-0.61\)