Question

A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. What is the expected value?

Short answer

The expected value is$E\left(x\right)=2.32$

Step-by-step solution

Content Introduction

A discrete probability distribution counts events with finite or countable outcomes. Discrete distributions, on the other hand, depict data with a countable number of outcomes, i.e., the alternative outcomes may be listed. It's possible that the list will be finite or limitless. A discrete distribution has two characteristics:

1. Each probability is between zero and one.
2. The sum of the probability is one.

Content Explanation

The expected value of the random variable is the probability weighted average of all possible values. The formula for finding the expected value is:

$$\begin{gathered} E\left(x\right)=\sum _{}\left(x\right).P\left(x\right) \\ E\left(x\right)=(0\times \frac{4}{50})+(0\times \frac{8}{50})+(0\times \frac{16}{50})+(0\times \frac{14}{50})+(0\times \frac{6}{50})+(0\times \frac{2}{50}) \\ E\left(x\right)=0+0.16+0.64+0.84+0.48+0.2 \\ E\left(x\right)=2.32 \end{gathered}$$