Question

3 A recent survey by a local municipality established that daily water usage by its households is normally distributed with a mean of 220 liters and a standard deviation of 45 liters.

(i) What percentage of households is likely to use more than 300 liters of water per day?

(ii) What is the probability of finding a household that uses less than 100 liters of water per day?

(iii) What percentage of households is likely to use between 300 to 350 liters of water per day?

Answer 1

(i)

$$P(X>300)=1-P(Z\le\dfrac{300-220}{45})$$

$$\approx1-P(Z\le1.7778)\approx0.0377$$

$3.77\%$

(ii)

$$P(X<100)=P(Z<\dfrac{100-220}{45})$$

$$\approx P(Z<-2.6667)\approx0.0038$$

$0.38\%$

(iii)

$$P(300<X<350)=P(Z<\dfrac{350-220}{45})$$

$$-P(Z\le\dfrac{300-220}{45})\approx P(Z<2.8889)$$

$$-P(Z\le1.7778)\approx0.0358$$

$3.58\%$