## The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a

Question

The mean gas mileage for a hybrid car is 56 miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of 3.2 miles per gallon.​

(a) What proportion of hybrids gets over 60 miles per​ gallon?

(b) What proportion of hybrids gets 52 miles per gallon or​ less?

(c )What proportion of hybrids gets between 57 and 62 miles per​ gallon?

(d) What is the probability that a randomly selected hybrid gets less than 45 miles per​ gallon?

in progress 0
2 weeks 2021-10-13T00:52:07+00:00 1 Answer 0

a) b) c) d) Step-by-step explanation:

1) Previous concepts

Normal distribution, is a “probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean”.

The Z-score is “a numerical measurement used in statistics of a value’s relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean”.

Let X the random variable that represent the gas mileage for a hybrid car of a population, and for this case we know the distribution for X is given by: Where and (a) What proportion of hybrids gets over 60 miles per​ gallon?

We are interested on this probability And the best way to solve this problem is using the normal standard distribution and the z score given by: If we apply this formula to our probability we got this:  And we can find this probability on this way: (b) What proportion of hybrids gets 52 miles per gallon or​ less?

We are interested on this probability And the best way to solve this problem is using the normal standard distribution and the z score given by: If we apply this formula to our probability we got this:  And we can find this probability on this way: (c )What proportion of hybrids gets between 57 and 62 miles per​ gallon?

We are interested on this probability And the best way to solve this problem is using the normal standard distribution and the z score given by: If we apply this formula to our probability we got this:  And we can find this probability on this way: (d) What is the probability that a randomly selected hybrid gets less than 45 miles per​ gallon?

We are interested on this probability And the best way to solve this problem is using the normal standard distribution and the z score given by: If we apply this formula to our probability we got this:  And we can find this probability on this way: 