Solve the problem.
-The number of new mini-vans sold by a particular salesperson during the month of March is exponentially distributed with a mean of 6. What is the probability that the salesperson will sell between 2 and 4 mini-vans in
March?
A) 0.130
B) 0.203
C) 0.250
D) 0.247

Question

Quizplus · Accepted Answer

If a random variable X is exponentially distributed with mean µ, then the probability density function of X is: f(x) = (1/µ) * e^(-x/µ), for x > 0 In this case, µ = 6, so: f(x) = (1/6) * e^(-x/6), for x > 0 To find the probability that the salesperson will sell between 2 and 4 mini-vans in March, we need to evaluate the integral of f(x) from x=2 to x=4: P(2 < X < 4) = ∫(2 to 4) [f(x) dx] = ∫(2 to 4) [(1/6) * e^(-x/6) dx] = [-e^(-x/6)](2 to 4) = -e^(-4/6) + e^(-2/6) = 0.203 Therefore, the probability that the salesperson will sell between 2 and 4 mini-vans in March is 0.203.

Solve the Problem. -The Number of New Mini-Vans Sold by a Particular Salesperson