Given a continuous uniform probability distribution with lim

Given a continuous uniform probability distribution with limits of 5 and 9, find the
Mean: rounded to 1 decimal place
First quartile: rounded to 1 decimal
Probability (6<=X<=8.5) rounded to 4 decimal places

Solution

For a uniform distirbution in the interval [a,b],

mean = (a+b)/2

first quartile = a + (b-a)/4

P(c<x<d) = (d-c)/(b-a)

Thus,

Mean = (5+9)/2 = 7 [answer]

first quartile = 5 + (9-5)/4 = 6 [answer]

P(6<=x<=8.5) = (8.5-6)/(9-5) = 0.625 [answer]