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erma4kov [3.2K]
3 years ago
5

Find the percent of area under a normal curve between the mean and the given number of standard deviations from the mean.​ (Note

that positive indicates above the​ mean, while negative indicates below the​ mean.)0.20
Mathematics
1 answer:
coldgirl [10]3 years ago
8 0

Answer:

15.86%

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Percent of area between the mean and 0.20 standard deviations from the mean:

pvalue of Z = 0.2 subtracted by the pvalue of Z = -0.2

Z = 0.2 has a pvalue of 0.5793

Z = -0.2 has a pvalue of 0.4207

0.5793 - 0.4207 = 0.1586

So this percentage is 15.86%

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