Respuesta :
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 = [tex]\frac{x-\mu}{\sigma}[/tex]
Since 85 is 0.25 standard deviations above the mean we have
[tex]0.25 = \frac{85-\mu}{\sigma}[/tex] or 0.25·σ = 85 - μ......1
1.5 = [tex]\frac{\mu-50}{\sigma}[/tex] 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 = [tex]\frac{80-x}{20}[/tex] which gives 15 = 80 - x or
x = 65.
