Consider a uniform distribution from a = 3 to b = 27.
(a) Find the probability that x lies between 5 and 18.
(b) Find the probability that x lies between 10 and 25.
(c) Find the probability that x lies between 7 and 15.
(d) Find the probability that x lies between 11 and 19.
(a) The probability that x lies between 5 and 18 is ______
(Round to three decimal places as needed.)
(A uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a < b), where a ≤ x ≤ b and all of the values of x are equally likely to occur. The probability density function of a uniform distribution is y = 1 / (b - a) on the interval from x = a to x = b. For any value of x less than a or greater than b, y = 0.
For two values c and d, where a ≤ c < d ≤ b, the probability that x lies between c and d is equal to the area under the curve between c and d, as shown. So, the area of the central shaded region equals the probability that x lies between c and d.)