Question

1. (No computer output is accepted) The mpg (miles per gallon) for all cars has a normal distribution with mean 100 km/L and standard deviation of 15 km/L.

a) Calculate the probability that any randomly selected car has an amount of mpg greater than 120 km/L.

b) Calculate the probability that any randomly selected car has an amount of mpg less than 95 km/L.

c) Calculate the probability that any randomly selected car has an amount of mpg between 93 km/L and 110 km/L.

d) A car is identified as a “best quality” if it is included in the top 2% of all mpgs. Find the minimum mpg needed to be qualified as “best quality”.

(Use 4 significant digits in your results. For example, if your answer is 20/7, write 2.8571. Moreover, do not leave the solution as 20/7. and , show your solutions in detail.)

Answer 1

Let X be a random variable representing the amount of mpg of a car. Then X has normal distribution with mean and standard deviation

a.  the probability that any randomly selected car has an amount of mpg greater than 120 km/L

=

b. the probability that any randomly selected car has an amount of mpg less than 95 km/L

=

c.  the probability that any randomly selected car has an amount of mpg between 93 km/L and 110 km/L

=

d. Let x= the minimum mpg needed to be qualified as “best quality”

So minimum mpg required 130.81 Km/L.

Here for all the questions   is a standard normal random variable with