Question

find the z - score such that the area under the standard normal curve to the left is 0.41.

• 0.23 is the z - score such that the area under the curve to the left is 0.41.

(round to two decimal places as needed.)

Explanation:

Step1: Use the standard normal distribution table (z - table)

We know that we need to find \(z\) such that \(P(Z<z)=0.41\).

Step2: Look up the value in the z - table

Looking at the standard normal distribution table (the body of the table contains the probabilities). We search for the value closest to \(0.41\).
The standard normal distribution table gives us the \(z\) - score. After looking up, we find that the \(z\) - score corresponding to a left - tail area of approximately \(0.41\) is \(z=- 0.23\) (by interpolating between the values in the table. For example, if we consider the rows and columns of the \(z\) - table: the area \(0.4090\) corresponds to \(z=-0.23\) and the area \(0.4147\) corresponds to \(z = - 0.22\). Since \(0.41\) is closer to \(0.4090\))

Answer:

\(-0.23\)