Question

14 fill in the blank 1 point the area to the left of z = 0.09 under the standard normal curve is (round to four decimal places as needed.)

Explanation:

Step1: Use the standard normal distribution table

The standard normal distribution table gives the cumulative probability (area to the left) for a given \(z\)-score. For \(z = 0.09\), we look up the value in the table.
In the standard normal table, we find the row corresponding to \(z = 0.0\) and the column corresponding to \(0.09\). The intersection of this row and column gives the cumulative probability.

Answer:

\(0.5359\)

(Note: There might be a slight difference in the value depending on the precision of the standard - normal table used. Some tables are more detailed. For example, using a more accurate calculation (such as using a calculator with a normal - distribution function \(P(Z<z)=\varPhi(z)\) where \(z = 0.09\)):

$$ \varPhi(0.09)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{0.09}e^{-\frac{t^{2}}{2}}dt\approx0.5359 $$

The value \(0.5395\) might be due to an error in table - reading or a less - precise table.)