Question

In a certain data distribution, 85 is 0.25 standard deviation above the mean and 50 is 1.5 standard deviations below the mean. What value is 0.75 standard deviation below the mean

Answer 1

Answer:

The mean is 80 and the standard deviation is 20. Therefore we have

65 is 0.75 standard deviation below the mean.

Step-by-step explanation:

z = $\frac{x-\mu}{\sigma}$

Since 85 is 0.25 standard deviations above the mean we have

$0.25 = \frac{85-\mu}{\sigma}$ or 0.25·σ  = 85 - μ......1

1.5 = $\frac{\mu-50}{\sigma}$ or 1.5·σ  = μ - 50..............2

From 1 we have σ = 340 - 4·μ substituting into 2 gives

1.5·(340 - 4·μ) =  μ - 50 ⇒ 510 - 6·μ = μ - 50

7·μ = 560 or μ = 80

Therefore σ = 340 - 4·μ = 340 - 4·80 = 20

A value, x, 0.75 standard deviation below the mean is given by

0.75 = $\frac{80-x}{20}$ which gives 15 = 80 - x or

x = 65.