Question

The mean of a normal probability distribution is 340; the standard deviation is 20.

1. About 68% of the observations lie between what two values?

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

3. Practically all of the observations lie between what two values?

Answer 1

Given mean =340
Standard deviation = 20

a) 68% of the observations lie between

About 68% of the area under the normal curve is within one standard deviation of the mean
i.e μ ± lσ
μ + lσ = 340+ 1(20) = 360
and
μ - lσ = 340 - 1(20) = 320

About 68% of the observations lie between 360 and 320.

b. 95% of the observations About 95% of the area under the normal curve is within one standard deviation of the mean

i.e μ ± 2σ

μ + 2σ= 340+ 2(20) = 380
and

μ - 2σ = 340 - 2(20) =300

About 95% of the observations lie between 380 and 300.

c)
Practically all of the area under the normal curve is within one standard deviation of the mean

i.e μ ± 3σ
μ + 3σ= 340+ 3(20) = 400
and
μ - 3σ = 340 - 3(20) = 280

Practically all of the observations lie between 400 and 280.