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 341. Assume this mileage follows the normal distribution with a standard deviation of 29 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 360 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 311 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 320 and 340 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 355 miles on the next tank of? gas? __

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

Answer 1

The distribution given here is:

a) The probability here is computed as:

Converting it to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.7438 is the required probability here.

b) P(X > 311)

Converting it to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.8495 is the required probability here.

c) P(320 < X < 340)

Converting it to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.2517 is the required probability here.

d) Probability here is computed as:

Therefore 0.0122 is the required probability here.