Question

find the indicated z score. the graph depicts the standard normal distribution with mean 0 and standard deviation 1.
the indicated z score is
(round to two decimal places as needed.)

Explanation:

Step1: Use the standard normal distribution table

We know that the area to the left of \(z = 0\) is \(0.5\). The given area in the right - tailed region (from \(z\) to \(0\)) is \(A=0.2514\). So the area to the left of \(z\) is \(P(Z\lt z)=0.5 - 0.2514=0.2486\).

Step2: Look up the \(z\) - value in the standard normal table

Looking up the value \(0.2486\) in the standard normal distribution table (the \(z\) - table). The closest value to \(0.2486\) in the body of the standard normal table. The \(z\) - value corresponding to an area of approximately \(0.2486\) is \(z=- 0.67\) (since the area is less than \(0.5\), \(z\) is negative).

Answer:

\(-0.67\)