Question

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?

Answer 1

a) (490,510)

b) (480,520)

c) (470,530)

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.