What hypothesis tests can be used on the normal distribution?

I have been studying the normal distribution, also known as the bell curve, and have made a few blog posts on it to chronicle my studies.

Normal distribution

The shape of the normal distribution is bell shaped and is characterised by two parameters, being the mean and the standard deviation.

The mean is the average of all of the data points and is the central point of the distribution.

The standard deviation tells the analyst how spread out the numbers are around the mean in a dataset, revealing how much the data varies from the mean. It plays a crucial role in determining the shape and spread of the distribution.

The standard deviation measures the distance between each data point from the mean and determines the width of the bell curve:-

1. A smaller standard deviation means that the data points are closer to the mean, resulting in a narrower bell curve.
2. A larger standard deviation means the data points are spread out, resulting in a wider bell curve.

The normal distribution is symmetrical, with most of the data clusters centring around the mean, or average.The normal distribution follows the empirical rule, where 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.