A gasoline tank for a certain car is designed to hold 14.0 gal of gas. Suppose t

Question

A gasoline tank for a certain car is designed to hold 14.0 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 14 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 13.85 gal? POx s 13.85) 0668 (b) What is the probability that a randomly selected tank will hold between 13.7 and 14.15 gal? 13.7 s x s 14.15) 9319 (c) If two such tanks are independently selected, what is the probability that both hold at most 14 gal? P(x s 14) 5 x

Explanation / Answer

Solution:

a)
P( x 13.85)
= 14
= 0.1
standardize x to z = (x - ) /
P(x < 13.85) = P( z < (13.85-14) / 0.1)
= P(z < -0.15) = 0.4404
(From Normal probability table)

b)
P( 13.7 x 14.15)
= 14
= 0.1
standardize x to z = (x - ) /
P( 13.7 < x < 14.15) = P[( 13.7 - 14) / 0.1 < Z < ( 14.15 - 14) / 0.1]
P( -0.3 < Z < 0.15) = 0.3821 - 0.5596 = -0.1775

c) P( X < 14 )
P( ( X - ) / < ( 14 - 14.0 ) / 0.1 )
= P( Z < 0 )
= 0.5
There are two tanks: 0.5*0.5 = 0.25

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