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 at 50.5 and the +1σ

Question

point is at 60.5. What is the normal model for the data distribution?(1 point)
Responses

(50.5,10)
open paren 50 point 5 comma 10 close paren

(50,10.5)
open paren 50 comma 10 point 5 close paren

(50.5,60.5)
open paren 50 point 5 comma 60 point 5 close paren

(50,60.5)

Answer 1

To determine the normal model for the data distribution, we first need to understand some key points from the information provided:

1. The mean of the data is 50.5.
2. The point corresponding to +1σ (one standard deviation above the mean) is 60.5.

To find the standard deviation (σ), we take the difference between the +1σ point and the mean:

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

Given that the mean is 50.5 and the standard deviation is 10, we can represent the normal distribution as \(N(\mu, \sigma)\) or \(N(50.5, 10)\).

Thus, the correct response for the normal model is:

(50.5, 10)