Questions: A survey of students at a university shows that 45% have a job. In a random sample of 700 students, find the mean and standard deviation for the number of students who have a job.

A survey of students at a university shows that 45% have a job. In a random sample of 700 students, find the mean and standard deviation for the number of students who have a job.

Transcript text: A survey of students at a university shows that $45 \%$ have a job. In a random sample of 700 students, find the mean and standard deviation for the number of students who have a job.

Solution

Solution Steps

Step 1: Calculate the Mean

The mean ($\mu$) for the number of students who have a job in a sample of 700 students, where 45% have a job, is calculated using the formula: \[ \mu = n \cdot p \] where $n = 700$ and $p = 0.45$.

\[ \mu = 700 \cdot 0.45 = 315 \]

Step 2: Calculate the Standard Deviation

The standard deviation ($\sigma$) is calculated using the formula: \[ \sigma = \sqrt{n \cdot p \cdot (1 - p)} \] where $n = 700$, $p = 0.45$, and $1 - p = 0.55$.

\[ \sigma = \sqrt{700 \cdot 0.45 \cdot 0.55} \approx 13.1624 \]

Final Answer

The mean and standard deviation for the number of students who have a job in a sample of 700 students are: \[ \mu = 315, \quad \sigma \approx 13.1624 \]

Thus, the correct answer is: \[ \boxed{\text{C}} \]

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