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Sagot :
Answer:
The area is 0.0316
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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
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