WHAT IS THE MEANING OF X~N(42,5,103.71)

X has a Normal (i.e. a Gaussian) probability distribution with mean 42.5 and a variance of 103.71. (That in turn means that it's got a standard deviation of sqrt(103.71) = 10.2, so since 95% of the distribution lies within the mean plus or minus about 2 standard deviations, 95% of the distribution lies between about 22.1 and 62.9)

The notation X ~ N(42, 5, 103.71) represents a random variable X that follows a normal distribution with a mean of 42, a standard deviation of 5, and a variance of 103.71.

To understand this notation better, let me break it down for you:

- "X" refers to the random variable we are interested in. In statistics, a random variable is a variable whose possible values are outcomes of a random phenomenon. It can take on different values according to the underlying probability distribution.

- "~" indicates that the random variable X follows a certain probability distribution. In this case, it follows a normal distribution.

- "N(42, 5, 103.71)" describes the specific normal distribution. The first parameter, 42, represents the mean (also known as the expected value) of the distribution. The mean is the central point around which the data is centered.

The second parameter, 5, is the standard deviation. It measures the spread or variability of the data points around the mean. A smaller standard deviation indicates that the data points are clustered closer to the mean, while a larger standard deviation means the data points are more spread out.

Lastly, the third parameter, 103.71, represents the variance, which is the square of the standard deviation. It measures the average squared distance from the mean.

In summary, the notation X ~ N(42, 5, 103.71) tells us that the random variable X follows a normal distribution with a mean of 42, a standard deviation of 5, and a variance of 103.71.