# Statistics - Describing distribution curve? - Easy solve

• IntegrateMe
This means that most of the sampled means will be around 8.1 ounces, with very few falling below 7.85 or above 8.15 ounces. In summary, the sampling distribution of x-bar has a normal shape with a center of 8.1 ounces and a spread of 0.05 ounces.
IntegrateMe
This should be a very easy problem, i just can't seem to find what makes the center, shape and spread.

The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is normal with mean 8.1 ounces and standard deviation 0.1 ounces. Company managers do not want the weight of a chocolate bar to fall below 7.85 ounces, for fear that consumers will complain.

Four candy bars are selected at random and their mean weight, x-bar, is computed.
Describe the center, shape, and spread of the sampling distribution of x-bar.

My method:

Mean of x-bar = Mean
So, the mean of x-bar = 8.1 ounces

Standard Deviation of x-bar = (standard deviation)/sqrt(n)
So, 0.1/sqrt(4) = 0.1/2 = 1/20

Okay, now the distribution curve for x-bar is going to have the characteristics of mean = 8.1 and standard deviation = 0.05. I've gotten that far, but now i don't know how to describe the center (I'm assuming this is 8.1?), shape, and spread or the distribution curve?

Any help?

The center of the distribution curve is 8.1 ounces, the shape is normal and the spread is 0.05 ounces.

## What is a distribution curve?

A distribution curve, also known as a frequency distribution or probability distribution, is a graphical representation of the frequency or probability of different values occurring in a dataset.

## What is the purpose of describing a distribution curve?

The purpose of describing a distribution curve is to summarize and understand the data, as well as to make predictions and inferences about the population from which the data was collected.

## What are the main characteristics of a distribution curve?

The main characteristics of a distribution curve include its shape, center, spread, and any outliers or unusual observations. These characteristics can be described using measures such as mean, median, mode, and standard deviation.

## How is a normal distribution curve different from other types of distribution curves?

A normal distribution curve, also known as a bell curve, is symmetric and has a characteristic bell shape. It is often used to model natural phenomena and many statistical tests assume that the data follows a normal distribution. Other types of distribution curves may be skewed or have multiple peaks, indicating a non-normal distribution of data.

## How can I determine if a dataset follows a normal distribution?

There are several ways to determine if a dataset follows a normal distribution, such as visual inspection of a histogram or box plot, or conducting a statistical test such as the Shapiro-Wilk test. However, it is important to note that even if a dataset appears to follow a normal distribution, it is still necessary to confirm this with statistical tests before making any assumptions or inferences.

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