Question

What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question. A normal curve with a peak at 0 is shown. The area under the curve shaded is negative 2 to negative 1. Z Probability 0. 00 0. 5000 1. 00 0. 8413 2. 00 0. 9772 3. 00 0. 9987 0. 02 0. 14 0. 34 0. 84.

Answer 1

The area under the shaded region from 1 to 2 is 0.14

What will be the shaded region area?

Probabilities actually define the percentage of the happening of an event

Here the shaded region shows  the probability of the z-scores

The shaded region 1 to 2 is represented as:

$P(1 < z < 2)$

By using the probability of z-score we can have

$P(1 < z < 2)=P(z < 2)-P(z < 1)$

From the given standard normal table:

$P(z < 2)=0.9772$

$P(z < 1)=0.8413$

So, we have:

$P(1 < z < 2)=0.9772-0.8413$

$P(1 < z < 2)=0.1359$

The approximated value will be

$P(1 < z < 2)=0.14$

Thus the area under the curve shaded is 1 to 2 is 0.14

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