What Is the Probability That It Will Take Less Than $\mu$

question 33

Multiple Choice

What is the probability that it will take less than or equal to 0.25 hours to service any call based on the following exponential probability distribution with rate $\mu$ = 5?
$\begin{array}{llcc} \quad\quad\text { Average Service Rate } &\\\hline \text { \(\mu\) =5 } &\text { per hour} &\\\end{array}$

$\begin{array}{cc}\mathrm{T} & \mathrm{P}(\text { service time } \leq \mathrm{T}) \\\hline 0.00 & 0.00 \\0.05 & 0.22 \\0.10 & 0.39 \\0.15 & 0.53 \\0.20 & 0.63 \\0.25 & 0.71 \\0.30 & 0.78 \\0.35 & 0.83 \\0.40 & 0.86 \\0.45 & 0.89 \\0.50 & 0.92 \\0.55 & 0.94 \\0.60 & 0.95 \\0.65 & 0.96\end{array}$

• A) 0.00
• B) 0.71
• C) 0.92
• D) 1.00

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Definitions:

Critical-Thinking Attitude

An approach that involves objective analysis and evaluation of an issue to form a judgment.

Caring Attitude

An approach that embodies compassion, concern, and consideration for others, showing support and understanding in a healthcare context.

Client's Crying

An emotional response or manifestation of feelings of distress, sadness, or joy in a therapeutic or caregiving environment.

Critical Thinking

The objective analysis and evaluation of an issue in order to form a judgment, crucial in problem solving and decision-making processes.