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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?

Respuesta :

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

[tex]\mu \pm \sigma\\=500 \pm 10\\=(490, 510)[/tex]

About 68% of data lies within 490 and 510.

b) 95% of the observations

[tex]\mu \pm 2\sigma\\=500 \pm 2(10)\\=(480, 520)[/tex]

About 95% of data lies within 480 and 520.

c) All the observations

[tex]\mu \pm 3\sigma\\=500 \pm 3(10)\\=(470, 530)[/tex]

All of the observations lie between 470 and 530.

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