Question
In: Statistics and Probability
1. (No computer output is accepted) The mpg (miles per gallon) for all cars has a...
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.)
Solutions
Expert Solution
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 
orchestra answered 2 years agoRelated Solutions
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