The average number of miles driven on a full tank of gas in a certain model car

Question

The average number of miles driven on a full tank of gas in a certain model car before its? low-fuel light comes on is 345. Assume this mileage follows the normal distribution with a standard deviation of 28 miles. Complete parts a through d below.

a. What is the probability? that, before the? low-fuel light comes? on, the car will travel less than 363 miles on the next tank of? gas?

(Round to four decimal places as? needed.)

b. What is the probability? that, before the? low-fuel light comes? on, the car will travel more than 301 miles on the next tank of? gas?

(Round to four decimal places as? needed.)

c. What is the probability? that, before the? low-fuel light comes? on, the car will travel between 318 and 338 miles on the next tank of? gas?

?(Round to four decimal places as? needed.)

d. What is the probability? that, before the? low-fuel light comes? on, the car will travel exactly 366 miles on the next tank of? gas?

(Round to four decimal places as? needed.)

Explanation / Answer

Solution:- Given that mean = 345, sd = 28

a. P(X < 363) = P((x-?)/? < (363-345)/28)

= P(Z < 0.6429)

= 0.7389

b. P(X > 301) = P(Z > (301-345)/28)

= P(Z > -1.5714)

= 0.9418

c. P(318 < X < 338) = P((318-345)/28 < Z < (338-345)/28)

= P(-0.9643 < Z <  -0.25)

=  0.2328

d P(X = 366) = 0

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