Answer:
Explanation:
The range of the uniform distribution is from 23 to 47, so the minimum value (a) is 23 and the maximum value (b) is 47.
The probability density function for a uniform distribution is:
f(x) = 1 / (b - a) if a ≤ x ≤ b
= 0 otherwise
We want to find the probability that a random vehicle gets between 28 and 36 miles per gallon. This is the same as finding the area under the probability density function between x = 28 and x = 36.
Since the distribution is uniform, the probability density function is a horizontal line between x = 23 and x = 47, with height equal to 1 / (47 - 23) = 1/24.
The area under the probability density function between x = 28 and x = 36 is:
P(28 ≤ x ≤ 36) = (36 - 28) * 1/24 = 8/24 = 1/3
Therefore, the probability that a random vehicle gets between 28 and 36 miles per gallon is 1/3, or 0.3333 rounded to four decimal places.