About ______% of the area is between z= -1 and z= 1 (or within 1 standard deviation of the mean)? How do you solve this?

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TaeKwonDoIsDead TaeKwonDoIsDead · Answer 1 · 2019-10-08T19:18:45+02:00

Answer:

68%

Step-by-step explanation:

68-95-99.7% Rule:

This is the empirical rule which is used to remember the percentage of values that is within a band of the mean. We say:

Clearly, from the empirical rule, we see that about 68% of the area is between z = -1 and z = 1 (or within 1 standard deviation of the mean)

fichoh fichoh · Answer 2 · 2021-10-01T17:58:51+02:00

The percentage of area within 1 standard deviation of the mean of a normal curve is 68%

To obtain the percentage of area within One - standard deviation of the mean :

P(-1 ≤ Z ≤ 1) = P(Z < 1) - P(Z < - 1)

The percentage of the area below 1 standard deviation of the mean ; P(Z < 1) = 0.84134

The percentage of the area below - 1 standard deviation of the mean ; P(Z < - 1) = 0.15866

Therefore,

P(Z < 1) - P(Z < - 1) = (0.84134 - 0.15866) = 0.68268 = 68.3%

Therefore, about 68% of the area under a normal curve is within 1 standard deviation of the mean

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