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

Answers

Answer 1

The approximate area of the shaded region under the standard normal curve is 0.0793.

The standard normal table shows the probabilities for various z-scores. To find the area under the curve between z = -2 and z = -1, we need to find the area to the left of z = -1 and subtract the area to the left of z = -2.

Using the table, we find that the probability to the left of z = -1 is 0.1587 and the probability to the left of z = -2 is 0.0228. Subtracting 0.0228 from 0.1587 gives us the approximate area of the shaded region, which is 0.1359.

However, since the shaded region is to the left of the mean, which is 0, we need to subtract this value from 0.5 (the total area to the left of the mean) to get the final answer of 0.0793. Therefore, the approximate area of the shaded region under the standard normal curve is 0.0793.

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