Question

Marcus is examining a histogram based on a dataset. He notices that the data is roughly symmetrical around a single peak at 50. The mean of the data is 50.5, and the +1σ point is at 60.5. What is the normal model for the data distribution?
A. (50, 10.5)
B. (50.5, 10)
C. (50.5, 60.5)
D. (50, 60.5)

Answer 1

To determine the normal model for the data distribution, we need to identify the mean and standard deviation.

1. **Mean**: The mean of the data is given as 50.5.
2. **Standard Deviation**: The +1σ point is given as 60.5. In a normal distribution, the +1σ point is calculated as:

\[
\text{Mean} + \text{Standard Deviation} = \text{+1σ Point}
\]

So, we can set up the equation:

\[
50.5 + \sigma = 60.5
\]

From this, we can find the standard deviation (σ):

\[
\sigma = 60.5 - 50.5 = 10
\]

Now that we have both the mean (50.5) and the standard deviation (10), we can express the normal model for the data distribution.

The normal model is typically written as \( N(\mu, \sigma) \), where \( \mu \) is the mean and \( \sigma \) is the standard deviation.

Based on our findings:

- Mean (μ) = 50.5
- Standard Deviation (σ) = 10

This matches option **B: (50.5, 10)**.

So the answer is **B. (50.5, 10)**.