If the random variable X is exponentially distributed with parameter λ = 1.5,then the probability P(2 ≤ X ≤ 4) ,up to 4 decimal places,is

A) 0.6667
B) 0.0473
C) 0.5000
D) 0.2500

The probability density function (pdf) for an exponential distribution with parameter λ is given by:

f(x) = λe^(-λx), for x ≥ 0

Therefore, for our problem, we have:

P(2 ≤ X ≤ 4) = ∫2^4 λe^(-λx) dx

Using integration by substitution, we can simplify this to:

P(2 ≤ X ≤ 4) = (-1/λ) [e^(-λx)]2^4

= (-1/1.5) [e^(-1.5*4) - e^(-1.5*2)]

≈ 0.0473 (rounded to 4 decimal places)

Therefore, the answer is B.