Question

use technology to find the indicated area under the standard normal curve. include an appropriately labeled sketch of the normal curve and shade the appropriate region.
a. find the probability that a z - score will be 0.91 or less.
b. find the probability that a z - score will be 0.91 or more.
c. find the probability that a z - score will be between - 1.4 and - 1.04
the probability that a z - score will be 0.91 or less is 0.8186
(round to four decimal places as needed.)
b. which graph below shows the probability that a z - score is 0.91 or more?
the probability that a z - score will be 0.91 or more is
(round to four decimal places as needed.)

Explanation:

Step1: Use the property of the standard normal distribution

The total area under the standard normal curve is \(1\). We know from part (a) that \(P(Z\leq0.91) = 0.8186\).

Step2: Calculate \(P(Z\geq0.91)\)

By the formula \(P(Z\geq z)=1 - P(Z < z)\) (for continuous - distribution \(P(Z\leq z)=P(Z < z)\)). Here \(z = 0.91\), so \(P(Z\geq0.91)=1 - P(Z\leq0.91)\).
Substitute \(P(Z\leq0.91)=0.8186\) into the formula: \(P(Z\geq0.91)=1 - 0.8186\).

$$P(Z\geq0.91)=0.1814$$

Answer:

\(0.1814\)