What is the distribution with a mean of 0 and a standard deviation of 1 called?
Click on the arrows to vote for the correct answer
A. B. C. D. E.Explanation
These values describe the standard normal distribution.
The correct answer is E. Standard normal distribution.
The standard normal distribution is a specific type of probability distribution that has a mean of 0 and a standard deviation of 1. It is also known as the Gaussian distribution or the Z-distribution. In this distribution, the values are symmetrically distributed around the mean, with a bell-shaped curve.
The Z-score, mentioned in answer D, is a statistical measure that quantifies how many standard deviations an individual data point is from the mean of a distribution. It is calculated by subtracting the mean from the data point and then dividing the result by the standard deviation. The Z-score is commonly used in statistics to standardize data and compare different observations from various distributions. While the Z-score is related to the standard normal distribution, it is not the correct answer to the question.
Answer A, the binomial probability distribution, is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, where each trial has only two possible outcomes: success or failure. This distribution is not characterized by a mean of 0 and a standard deviation of 1, so it is not the correct answer.
Answer C, frequency distribution, refers to a tabular or graphical representation of data that shows the number of times a specific value or range of values occurs in a dataset. It is not related to a specific mean and standard deviation, so it is not the correct answer.
Answer B, "None of these answers," is not the correct answer because there is indeed a specific name for a distribution with a mean of 0 and a standard deviation of 1, which is the standard normal distribution.
In summary, the distribution with a mean of 0 and a standard deviation of 1 is called the standard normal distribution (also known as the Gaussian distribution or Z-distribution), which is represented by answer E.