Questions: A population of values has normal distribution μ=121.1 and σ=85.9 sample size =n=136 What is the mean of distribution? What is standard deviation?

A population of values has normal distribution μ=121.1 and σ=85.9 sample size =n=136 What is the mean of distribution? What is standard deviation?
Transcript text: A population of values has normal distribution $\mu=121.1$ and $\sigma=85.9$ sample size $=n=136$ What is the mean of distribution? What is standard deviation?
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Solution

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Solution Steps

Step 1: Mean of the Distribution

The mean of the population is given as \( \mu = 121.1 \). Therefore, the mean of the distribution is:

\[ \text{Mean of the distribution} = 121.1 \]

Step 2: Standard Deviation of the Distribution

The standard deviation of the population is given as \( \sigma = 85.9 \). To find the standard deviation of the sample mean (also known as the standard error), we use the formula:

\[ \text{Standard Error} = \frac{\sigma}{\sqrt{n}} = \frac{85.9}{\sqrt{136}} \]

Calculating this gives:

\[ \text{Standard Error} \approx 7.37 \]

Final Answer

The answers to the questions are:

  • Mean of the distribution: \( \boxed{121.1} \)
  • Standard deviation (standard error) of the distribution: \( \boxed{7.37} \)
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