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 (99.7%) of the observations lie between what two values?

a) About 68% of the observations lie between 490 and 510

b) About 95% of the observations lie between 480 and 520

c) All (99.7%) of the observations lie between 470 and 530

Step-by-step explanation:

We solve this question using the empirical rule formula

This states that:

• 68% of data falls within 1 standard deviations from the mean - between μ – σ and μ + σ .

• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

From the 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?

Hence,

μ – σ

= 500 - 10

= 490

μ + σ

= 500 + 10

= 510

About 68% of the observations lie between 490 and 510

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

Hence, from the above formula's

μ – 2σ

= 500 - 2(10)

= 500 - 20

= 480

μ + 2σ

= 500 + 2(10)

= 500 + 20

= 520

About 95% of the observations lie between 480 and 520

c. Practically all (99.7%) of the observations lie between what two values?

μ – 3σ

500 - 3(10)

500 - 30

= 470

μ + 3σ

= 500 + 3(10)

= 500 + 30

= 530

All (99.7%) of the observations lie between 470 and 530

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step-by-step explanation:

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