Question

If 75% of all families spend more than $75 weekly for food, while 15% spend more than $150, what is the mean weekly expenditure and what is the standard deviation? (assume normal distribution.)

Answer 1

Z at 75% ≈ 0.674. Since the spending is more than $75, Z = -0.674
Z at 15% ≈ - 1.036. Since the spending is more than $150, Z = 1.036

Now,
Z = (x-mean)/SD => Z*SD = x-mean

Therefore,
-0.674*SD = 75 - mean ------- (1)
1.036*SD = 150 -mean ------- (2)
---------------------------------------------
(1) - (2)
-1.71SD = - 75 => SD = 75/1.71 = 43.8596

Substituting SD in (1) => -0.674*43.8596 = 75 -mean => mean = 75+(0.674*43.8596) = 104.46.

Then,
SD = 43.86, mean = 104.46