Why do we need the process of Standardisation when we calculate probabilities for any normal distribution?

Standardisation of a normal variate does not affect the characteristics of the distribution and hence we can use it as a standard distribution which we can apply for different normal distributions to compute required probabilities.

What requirements are necessary for a normal probability distribution to be a standard?

The mean must have a mean of 0 and a standard deviation of 1. What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? It is the z score with an area of alpha to its right. What does the notation of Zalpha indicate?

What is the difference between a standard normal distribution and a non standard normal distribution?

The standard normal distribution has a mean of 0 and a standard deviation of​ 1, while a nonstandard normal distribution has a different value for one or both of those parameters.

What advantage could possibly be gained from converting a normal distribution into a standard format?

Converting a normal distribution into the standard normal distribution allows you to: Compare scores on different distributions with different means and standard deviations. Normalize scores for statistical decision-making (e.g., grading on a curve).

What is the significance of the mean of a probability distribution?

Answer: The significance of the mean of a probability distribution is it gives the expected value of a discrete random variable.

How do you convert normal distribution to standard normal distribution?

Keep in mind! Any normal distribution can be transformed to standard normal distribution by the formula: 𝑧 = 𝑥−𝜇 �� where x-score, 𝜇-mean and 𝜎-standard deviation. Each of the values obtained using the given formula is called z-scores.

What is the proportion of standard normal variates within 2-3 standard deviations?

The proportion of standard normal variates contained within 1, 2, and 3 standard deviations from the mean is 68.3\%, 95.4\%, and 99.7\%, respectively; 2.

What is an example of a normal random variable?

Convert from standard scores to normal random variable ◦ Example: A highly selective university only admits the top 5\% of the total examinees in their entrance exam. The results of this year’s entrance exam follow a normal distribution with the mean of 285 and a standard deviation of 12.

Why normalize data to have zero mean and unit standard deviation?

Normalizing data to have zero mean and unit standard deviation (subtracting the mean, then scaling by the inverse of the standard deviation) makes it possible to use the same tools on data that were originally very different.