What is the designation for the standard normal random variable?

What is the designation for the standard normal random variable?

• A. z
• B. n
• C. x
• D. p

Answer: (A)

The standard normal random variable is designated as "z." This designation comes from the standard normal distribution, which is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. The "z" score indicates how many standard deviations a particular observation is from the mean. In statistics, the concept of standardization involves transforming any normal variable into a standard normal variable by subtracting the mean and dividing by the standard deviation, resulting in the z-score. This process allows for comparison between different datasets and simplifies calculations regarding probabilities and critical values. Other options such as "n," "x," and "p" represent different statistical concepts; for instance, "n" often refers to sample size, "x" could denote individual observations from a dataset, and "p" commonly signifies a proportion or probability. Thus, the use of "z" is specifically tied to the context of standard normal distributions and is essential in statistical analyses involving z-scores.

The standard normal random variable is designated as "z." This designation comes from the standard normal distribution, which is a special case of the normal distribution with a mean of 0 and a standard deviation of 1. The "z" score indicates how many standard deviations a particular observation is from the mean.

In statistics, the concept of standardization involves transforming any normal variable into a standard normal variable by subtracting the mean and dividing by the standard deviation, resulting in the z-score. This process allows for comparison between different datasets and simplifies calculations regarding probabilities and critical values.

Other options such as "n," "x," and "p" represent different statistical concepts; for instance, "n" often refers to sample size, "x" could denote individual observations from a dataset, and "p" commonly signifies a proportion or probability. Thus, the use of "z" is specifically tied to the context of standard normal distributions and is essential in statistical analyses involving z-scores.