Question

Find the area under the standard normal curve that lies outside the interval between z = -2.16 and z = 2.14​

Answer 1

The area is 0.0316

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X

Find the area under the standard normal curve that lies outside the interval between z = -2.16 and z = 2.14

Below z = -2.16 or Above z = 2.14

Below z = -2.16

z = -2.16 has a pvalue of 0.0154, which means that this area is 0.0154

Above z = 2.14

z = 2.14 has a pvalue of 0.9838, which means that this area is 1 - 0.9838 = 0.0162

Total:

0.0154 + 0.0162 = ​0.0316

The area is 0.0316