Answer to Question #342951 in Statistics and Probability for yaoo

Question #342951

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. 



1
Expert's answer
2022-05-20T10:53:37-0400

Given μ=21.3,s=3.4\mu=21.3, s=3.4

(a)


P(X30)=1P(Z<3021.33.4)P(X\ge30)=1-P(Z<\dfrac{30-21.3}{3.4})




1P(Z<2.5588)0.00525\approx1-P(Z<2.5588)\approx0.00525



(b)


P(20X25)=P(Z2521.33.4)P(20\le X\le 25)=P(Z\le\dfrac{25-21.3}{3.4})




P(Z<2021.33.4)P(Z1.0882)-P(Z<\dfrac{20-21.3}{3.4})\approx P(Z\le1.0882)

P(Z<0.3824)0.861750.35108-P(Z<-0.3824)\approx0.86175-0.35108

0.861750.351080.5107\approx0.86175-0.35108\approx0.5107

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