Mathematics: The mean of a normal probability distribution is 500; the standard deviation is 10. (a) About 68% of the observations lie between what two values? (b) About 95% of the observations lie between what two values? (c) Practically all of the observations lie between what two values?

-2/3Step-by-step explanation:...

The mean of a normal probability distribution is 500;

Ответ:

courtneywick

18.01.2022

Mathematics

a) (490,510)

b) (480,520)

c) (470,530)

Step-by-step explanation:

Mean, μ = 500

Standard Deviation, σ = 10

Empirical Rule:

According to Empirical rule almost all data lies within three standard deviation of mean for a normal distribution.About 68% of data lies within one standard deviation of the mean.About 95% of data lies within two standard deviation of mean.About 99.7% of data lies within three standard deviation of mean.

a) 68% of the observations

$\mu \pm \sigma\\=500 \pm 10\\=(490, 510)$

About 68% of data lies within 490 and 510.

b) 95% of the observations

$\mu \pm 2\sigma\\=500 \pm 2(10)\\=(480, 520)$

About 95% of data lies within 480 and 520.

c) All the observations

$\mu \pm 3\sigma\\=500 \pm 3(10)\\=(470, 530)$

All of the observations lie between 470 and 530.

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The mean of a normal probability distribution is 500; the standard deviation is 10.
(a) About 68% of the observations lie between what two values?

(b) About 95% of the observations lie between what two values?

(c) Practically all of the observations lie between what two values?

Ответ:

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