Question

1)A cab driver knows from experience that the number of fares he will pick up in an evening is a random variable with µ = 21.3 and s = 3.4 Assuming that the distribution of this random variable can be approximated closely with a normal curve, find the probabilities that in an evening the driver will pick up (a) at least 30 fares (b) anywhere from 20 to 25 fares inclusively. 

Answer 1

Given $\mu=21.3, s=3.4$

(a)

$$P(X\ge30)=1-P(Z<\dfrac{30-21.3}{3.4})$$

$$\approx1-P(Z<2.5588)\approx0.00525$$

(b)

$$P(20\le X\le 25)=P(Z\le\dfrac{25-21.3}{3.4})$$

$$-P(Z<\dfrac{20-21.3}{3.4})\approx P(Z\le1.0882)$$

$$-P(Z<-0.3824)\approx0.86175-0.35108$$

$$\approx0.86175-0.35108\approx0.5107$$