Suppose that the random variable x has a uniform distribution with c = 2 and d = 8.
a. Write the formula for the probability curve of x, and write an interval that gives the possible values of x.
b. Graph the probability curve of x.
c. Find P(3 ≤ x ≤ 5).
d. Find P(1.5 ≤ x ≤ 6.5).
e. Calculate the mean μx, variance σ2x, and standard deviation σx.
f. Calculate the interval [μx ± 2σx]. What is the probability that x will be in this interval?