Question

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The average gas mileage of a certain model car is 28 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 1.5, find the probability that a car has a gas mileage of between 25.8 and 29.3 miles per gallon.

a. 0.18

b. 0.20

c. 0.15

d. 0.26

e. 0.48

f. 0.74

g. None of the above

Answer 1

SOLUTION:

From given data,

The average gas mileage of a certain model car is 28 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 1.5, find the probability that a car has a gas mileage of between 25.8 and 29.3 miles per gallon.

Mean = = 28

Standard deviation = = 1.5

Z = (X - ) / = (X - 28 ) / 1.5

The probability that a car has a gas mileage of between 25.8 and 29.3 miles per gallon.

P( 25.8 < X < 29.3 )
= P( (25.8 - 28 ) / 1.5 < Z < (29.3 - 28 ) / 1.5 )
= P(-1.46 < Z < 0.86 )
= P(Z < 0.86) - P( Z < -1.46)
=  0.80511 - 0.07215 ( using std normal table)
=  0.74

Answer : Option (f)