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 "\\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"

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