1. Explain the Bell-shaped curve? 2. What is the difference between the Normal Distribution and the...

1. Explain the Bell-shaped curve?

2. What is the difference between the Normal Distribution and the Standard Normal Distribution?

Solutions

Expert Solution

1. It shall be noted that a Bell-Shaped curve is a graph depicting the normal distribution, which has a shape reminiscent of a bell. The top of the curve shows the mean, mode, and median of the data collected. Its standard deviation depicts the bell curve's relative width around the mean. It is perfectly symmetrical. It is concentrated around the peak and decreases on either side. In a bell curve, the peak represents the most probable event in the dataset while the other events are equally distributed around the peak. The peak of the curve corresponds to the mean of the dataset.

The dispersion of the data on the bell curve is measured by the standard deviation. The probabilities of the bell curve and the standard deviation share a few important relationships, including:

1) Around 68% of the data lies within 1 standard deviation.

2) Around 95% of the data lies within 2 standard deviations.

3) Around 99.7% of the data lies within 3 standard deviations.

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It shall be noted that a normal distribution with the mean 0 and standard deviation 1 is the standard normal distribution.

If the mean is not zero or the standard deviation is not 1, the symmetric distribution of the bell-shaped is called the (non-standard) normal distribution.

Rahul Sunny answered 1 year ago

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