Question

question 4 the standard normal random variable z is equal to

Explanation:

Step1: Recall standard - normal transformation

The formula for standardizing a normal random variable \(X\) (with mean \(\mu\) and standard deviation \(\sigma\)) to a standard - normal random variable \(Z\) is \(Z=\frac{X - \mu}{\sigma}\), where \(X\) is a value from the original normal distribution, \(\mu\) is the mean of the original normal distribution, and \(\sigma\) is the standard deviation of the original normal distribution.

Answer:

The standard normal random variable \(Z\) is equal to \(\frac{x-\mu}{\sigma}\) (assuming \(x\) is a value from the non - standard normal distribution with mean \(\mu\) and standard deviation \(\sigma\)). So the correct option is the one with the formula \(\frac{x - \mu}{\sigma}\) (the last option as indicated by the blue dot in the image).