Independent solution

How to solve this Exponential Distribution question

Setup

Setup

Convert the exponential mean into the corresponding rate parameter.

λ=12.50=0.40\lambda=\frac{1}{2.50}=0.40

Model

Model

The question asks for an upper-tail probability, so use the exponential survival function rather than its complement.

S(t)=Pr⁡(X≥t)=e−λtS(t)=\Pr(X\ge t)=e^{-\lambda t}

Compute

Compute

At a time equal to the distribution's mean, the rate-time product equals one.

Pr⁡(X≥2.50)=e−(0.40)(2.50)=e−1\Pr(X\ge2.50)=e^{-(0.40)(2.50)}=e^{-1}
e−1=0.3678794412…e^{-1}=0.3678794412\ldots

Answer

Answer

The required survival probability is the exponential constant e to the power negative one.

e−1(B)\boxed{e^{-1}\quad\text{(B)}}