A gasoline tank for a certain car is designed to hold 16.0 gal of gas. Suppose t

Question

A gasoline tank for a certain car is designed to hold 16.0 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 16 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 15.85 gal? P(x 15.85) = (b) What is the probability that a randomly selected tank will hold between 15.7 and 16.15 gal? P(15.7 x 16.15) = (c) If two such tanks are independently selected, what is the probability that both hold at most 16 gal? P(x 16)

Explanation / Answer

for normal distribution z score =(X-mean)/std deviaiton

(a) probability that a randomly selected tank will hold at most 15.85 ga =P(X<15.85)=P(Z<(15.85-16)/0.1)

=P(Z<-1.5) =0.0668

b)

probability that a randomly selected tank will hold between 15.7 and 16.15 =P(15.7<X<16.15)

=P((15.7-16)/0.1<Z<(16.15-16)/0.1)=P(-3<Z<1.5)=0.9332-0.0013 =0.9318

c) probability that one tank   hold at most 16 gal =P(X<16)=P(Z<(16-16)/0.1)=P(Z<0)=0.5

therefore due to independence probability that both hold at most 16 gal =0.5*0.5 =0.25

please revert for any clarification required,

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