Question

find the z - score such that the area under the standard normal curve to the left is 0.42.
is the z - score such that the area under the curve to the left is 0.42.
(round to two decimal places as needed.)

Explanation:

Step1: Use the standard normal distribution table or inverse - normal function

We know that if \(Z\) follows the standard normal distribution \(N(0,1)\), and we want to find \(z\) such that \(P(Z\lt z)=0.42\).
Using a standard normal table (or a calculator with an inverse - normal function, for example, on a TI - 84 Plus: invNorm(0.42,0,1)).

Step2: Look up the value

Looking up the value in the standard normal table (the body of the table contains probabilities \(P(Z\lt z)\)).
We find that \(z\approx - 0.20\)

Answer:

\(-0.20\)