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## Is Z is a standard normal variable find the probability?

For any normal random variable, we can transform it to a standard normal random variable by finding the Z-score. Then we can find the probabilities using the standard normal tables. For example, if is a standard normal random variable, the tables provide P ( Z ≤ a ) = P ( Z < a ) , for a constant, .

How do you find the Z values for the standard normal variable z?

z = (x – μ) / σ Assuming a normal distribution, your z score would be: z = (x – μ) / σ = (190 – 150) / 25 = 1.6.

What is the probability distribution standard normal variable z?

The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. Examine the table and note that a “Z” score of 0.0 lists a probability of 0.50 or 50%, and a “Z” score of 1, meaning one standard deviation above the mean, lists a probability of 0.8413 or 84%.

### What does it mean if Z is a standard normal variable?

Definition: standard normal random variable. A standard normal random variable is a normally distributed random variable with mean μ=0 and standard deviation σ=1. It will always be denoted by the letter Z. The density function for a standard normal random variable is shown in Figure 5.2. 1.

What is z-score probability?

The standard score (more commonly referred to as a z-score) is a very useful statistic because it (a) allows us to calculate the probability of a score occurring within our normal distribution and (b) enables us to compare two scores that are from different normal distributions.

What is a standard normal variable?

A standard normal random variable is a normally distributed random variable with mean μ=0 and standard deviation σ=1. It will always be denoted by the letter Z.

#### How to calculate the probability of a random variable?

A standard normal random variable Z is a normally distributed random variable with mean μ = 0 and standard deviation σ = 1. Probabilities for a standard normal random variable are computed using Figure 12.2 “Cumulative Normal Probability”. Use Figure 12.2 “Cumulative Normal Probability” to find the probability indicated.

How to find the z score of a random variable?

We can use the Standard Normal Cumulative Probability Table to find the z-scores given the probability as we did before. Area to the left of z-scores = 0.6000. The closest value in the table is 0.5987. The z-score corresponding to 0.5987 is 0.25.

Why do we use standard normal to find probabilities?

The standard normal is important because we can use it to find probabilities for a normal random variable with any mean and any standard deviation. But first, we need to explain Z-scores. We can convert any normal distribution into the standard normal distribution in order to find probability and apply the properties of the standard normal.

## What is the mean and standard deviation of a random variable?

To learn how to use Figure 12.2 “Cumulative Normal Probability” to compute probabilities related to a standard normal random variable. The normal random variable with mean 0 and standard deviation 1. is a normally distributed random variable with mean μ = 0 and standard deviation σ = 1. It will always be denoted by the letter Z.