Question

The forμla for converting a normally distributed random variable X to a Z-value is Z.

a) Mean
b) Median
c) Standard deviation
d) Variance

Answer 1

The formula for converting a normally distributed random variable X to a Z-value is Z = (X - µ) / σ, which calculates the z-score indicating how many standard deviations X is from the mean.

Step-by-step explanation:

The formula for converting a normally distributed random variable X to a Z-value is Z = (X - µ) / σ. This indicates that to find the Z-value, you subtract the mean (µ) of the distribution from the value of X and then divide the result by the standard deviation (σ) of the distribution. The Z-value, or z-score, thus represents how many standard deviations a value X is from the mean. When X follows a standard normal distribution, it is denoted as Z~ N(0, 1), signifying a mean of 0 and a standard deviation of 1.