Question

Find the z value such that the area under the standard normal distribution curve between 0 and z value is 0.3962 or 39.62%.

Answer 1

Using the normal distribution, it is found that z is Z = 1.26, given by option B.

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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 z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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, which is also the area under the normal curve to the left of Z. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X, which is also the area under the normal curve to the right of Z.

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• Area under the normal curve between 0 and the z-value is 0.3962.
• Z = 0 has a p-value of 0.5.
• Thus, we need to find z with a p-value of 0.5 + 0.3962 = 0.8962.
• Looking at the z-table, this is Z = 1.26, given by option B.

A similar problem is given at brainly.com/question/22940416

Answer 2

the answer is b