Questions: A division of a company has over 200 employees, 40% of which are male. Each month, the company randomly selects 8 of these employees to have lunch with the CEO. What are the mean and standard deviation of the number of males selected each month? You may round your answers to the nearest tenth. mean: 3.2 males standard deviation: males

A division of a company has over 200 employees, 40% of which are male. Each month, the company randomly selects 8 of these employees to have lunch with the CEO. What are the mean and standard deviation of the number of males selected each month? You may round your answers to the nearest tenth. mean: 3.2 males standard deviation: males
Transcript text: A division of a company has over 200 employees, $40 \%$ of which are male. Each month, the company randomly selects 8 of these employees to have lunch with the CEO. What are the mean and standard deviation of the number of males selected each month? You may round your answers to the nearest tenth. mean: 3.2 $\square$ males standard deviation: $\square$ males
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Solution

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Solution Steps

Step 1: Define the Problem

We are tasked with finding the mean and standard deviation of the number of males selected from a division of a company with over 200 employees, where \( 40\% \) of the employees are male. Each month, 8 employees are randomly selected to have lunch with the CEO.

Step 2: Identify Parameters

In this scenario, we can define the parameters for the binomial distribution:

  • Number of trials \( n = 8 \) (the number of employees selected each month).
  • Probability of success \( p = 0.4 \) (the probability that a selected employee is male).
  • Probability of failure \( q = 1 - p = 0.6 \).
Step 3: Calculate the Mean

The mean \( \mu \) of a binomial distribution is calculated using the formula: \[ \mu = n \cdot p \] Substituting the values: \[ \mu = 8 \cdot 0.4 = 3.2 \]

Step 4: Calculate the Variance

The variance \( \sigma^2 \) of a binomial distribution is given by: \[ \sigma^2 = n \cdot p \cdot q \] Substituting the values: \[ \sigma^2 = 8 \cdot 0.4 \cdot 0.6 = 1.92 \]

Step 5: Calculate the Standard Deviation

The standard deviation \( \sigma \) is the square root of the variance: \[ \sigma = \sqrt{n \cdot p \cdot q} = \sqrt{1.92} \approx 1.3856 \approx 1.4 \]

Final Answer

The mean number of males selected each month is \( 3.2 \) and the standard deviation is \( 1.4 \).

Thus, the final answers are: \[ \boxed{\text{Mean: } 3.2 \text{ males}} \] \[ \boxed{\text{Standard Deviation: } 1.4 \text{ males}} \]

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