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 14.8 gal? P(x 14.8) = (b) What is the probability that a randomly selected tank will hold between 14.7 and 15.15 gal? P(14.7 x 15.15) = (c) If two such tanks are independently selected, what is the probability that both hold at most 15 gal? P(x 15) =

Explanation / Answer

Ans:

Given that

mean =15

standard deviation=0.1

z=(x-15)/0.1

a)

z=(14.8-15)/0.1=-0.2/0.1=-2

P(x<=14.8)=P(z<=-2)=0.0228

b)

For x=14.7

z=(14.7-15)/0.1=-3

For x=15.15

z=(15.15-15)/0.1=0.15/0.1=1.5

So,

P(14.7 x 15.15) =P(-3<=z<=1.5)

=P(z<=1.5)-P(z<=-3)

=0.9332-0.0013=0.9319

c)P(x<=15)=P(z<=0)=0.5

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

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