A gasoline tank for a certain car is designed to hold 15.0 gal of gas. Suppose t

Question

A gasoline tank for a certain car is designed to hold 15.0 gal of gas. Suppose that the variable x = actual capacity of a randomly selected tank has a distribution that is well approximated by a normal curve with mean 15 gal and standard deviation 0.1 gal. (Round all answers to four decimal places.)

(a) What is the probability that a randomly selected tank will hold at most 14.85 gal?
P(x 14.85) =  

(b) What is the probability that a randomly selected tank will hold between 14.7 and 15.2 gal?
P(14.7 x 15.2) =  

(c) If two such tanks are independently selected, what is the probability that both hold at most 15 gal?
P(x 15) =

Explanation / Answer

a) P(X<14.85)=P(Z<(14.85-15)/0.1)=P(Z<-1.5) =0.0668

b)P(14.7<X<15.2)=P(-3<X<2)=0.97725-0.00135 =0.9759

c)P(X<=15) =0.5 for one tank as 15 is at mean and normal distribution is symmetrical

hence probability that  both hold at most 15 gal =0.5*0.5=0.25

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