Question

The mean of a normal probability distribution is 500; the standard deviation is 10.

Answer 1

Answer:

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.