Question

find the area of the shaded region. the graph depicts the standard normal distribution with mean 0 and standard deviation 1. (round to four decimal places as needed.) find the area of the indicated region under the standard normal curve. (round to four decimal places as needed.)

Explanation:

Step1: Use the standard normal distribution table

The area to the left of \(z = 0.66\) is found using the standard - normal table. For \(z=0.66\), we look up the value in the table. The value corresponding to \(z = 0.66\) is \(0.7454\).

Step2: Analyze the second problem

For the standard normal distribution, the area between \(z = 0\) and \(z=0.7\). We know that the area to the left of \(z = 0\) is \(0.5\) (by the property of the standard normal distribution, since it is symmetric about \(z = 0\)). The area to the left of \(z=0.7\) is found using the standard - normal table. Looking up \(z = 0.7\) in the standard - normal table, we get \(P(Z<0.7)=0.7580\). Then the area between \(z = 0\) and \(z = 0.7\) is \(P(0<Z<0.7)=P(Z < 0.7)-P(Z < 0)\).

Answer:

For the first problem (area to the left of \(z = 0.66\)): \(0.7454\)
For the second problem (area between \(z = 0\) and \(z=0.7\)): \(0.7580 - 0.5=0.2580\)