Question

Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The probability that a random vehicle gets between 25 and 34 miles per gallon is: Answer: (Round to one decimal place)

Answer 1

The probability that a random vehicle gets between 25 and 34 miles per gallon is 0.9.

Step-by-step explanation:

To find the probability that a random vehicle gets between 25 and 34 miles per gallon, we need to determine the proportion of the uniform distribution that falls within that range.

The range of the uniform distribution is from 25 to 35, so the total span is 35 - 25 = 10. The sub-range from 25 to 34 has a span of 34 - 25 = 9.

Therefore, the probability is 9/10 = 0.9, rounded to one decimal place.

Answer 2

0.9 = 90%

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d is given by the following formula.

`P(c \leq X \leq d) = (d - c)/(b-a)`

Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35.

This means that
`a = 25, b = 35`

The probability that a random vehicle gets between 25 and 34 miles per gallon is:

`P(25 \leq X \leq 34) = (34 - 25)/(35 - 25) = 0.9`

So the answer is 0.9 = 90%