Question

for the standard normal variable z, find z0.57, the value that divides the area under the density curve into 0.43 to the left and 0.57 to the right.
z0.57 = (round the answer to 2 decimal places)

Explanation:

Step1: Use standard - normal table

We know that the standard - normal table gives the cumulative distribution function $\varPhi(z)$ which is the area to the left of $z$. We want to find $z_{0.57}$ such that the area to the left is $0.43$. Looking up the value $0.43$ in the body of the standard - normal table (the $z$ - table).

Step2: Identify the $z$ - value

From the standard - normal table, the $z$ - value corresponding to an area of $0.43$ to the left is approximately $z=-0.18$.

Answer:

$-0.18$