A call center technical specialist spends varying amount of time in each call to resolve the concern. The time spent in each call is modeled using the following distribution: X~ Exp (0.2).Find P (2 < x < 10):Question 14Answera.0.5350b.0.6350c.0.2350
Question
A call center technical specialist spends varying amount of time in each call to resolve the concern. The time spent in each call is modeled using the following distribution: X~ Exp (0.2).Find P (2 < x < 10):Question 14Answera.0.5350b.0.6350c.0.2350
Solution
The given distribution is an exponential distribution. The exponential distribution has a probability density function (PDF) given by f(x|λ) = λe^(-λx) for x >= 0, and 0 otherwise. Here, λ = 0.2.
The cumulative distribution function (CDF), which gives the probability that a random variable is less than or equal to a certain value, is given by F(x|λ) = 1 - e^(-λx).
We want to find P(2 < X < 10). This is equal to F(10) - F(2).
Substituting the given λ into the CDF:
F(10) = 1 - e^(-0.210) = 1 - e^-2, F(2) = 1 - e^(-0.22) = 1 - e^-0.4.
Therefore, P(2 < X < 10) = F(10) - F(2) = (1 - e^-2) - (1 - e^-0.4) = e^-0.4 - e^-2.
Calculating these values gives approximately 0.6703 - 0.1353 = 0.5350.
So, the answer is a. 0.5350.
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