Question

modeling with normal distributions quick check
harvest is meanuring a histogrom based on a dataset he notices that the data is roughly symmetricol around a single peak at 50. the mean of the data is at 60.5 and the + for point is at 60.5. what is the normal model for the data distribution?
(1 point)
(50, 18.5)
(60.5, 10)
(50, 60.5)
(60.5, 60.5)

Explanation:

Step1: Recall the parameters of a normal model

A normal model is represented as \(N(\mu,\sigma)\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Step2: Identify the mean

The mean \(\mu\) of the data is given as \(60.5\).

Step3: Identify the standard deviation

In a normal distribution, the peak of the histogram (the mode) is equal to the mean. The standard - deviation can be found using the relationship for a normal distribution. If we assume that the data is symmetric around the mean. Here, we can use the fact that for a normal model, the standard deviation is calculated based on the spread. If the mean is \(60.5\) and we assume a simple calculation (since the problem gives limited information but in a normal model representation \(N(\mu,\sigma)\)), and if we consider the options:
The normal model is written as \(N(\mu,\sigma)\) where \(\mu = 60.5\) (mean) and \(\sigma= 10\) (a common - sense check of the options, as \(N(60.5,10)\) is in the form of mean and standard deviation)

Answer:

\((60.5,10)\)