Final answer:
In a standard normal distribution, the probability of a random variable Z being less than a certain value can be calculated using the cumulative distribution function (CDF) or a Z-score table.
Step-by-step explanation:
The question is about the standard normal distribution. In a standard normal distribution, a random variable Z is normally distributed with a mean of 0 and a standard deviation of 1. The probability of Z being less than a certain value can be calculated using the cumulative distribution function (CDF) of the standard normal distribution.
To find P(Z<x), we can use the CDF function or lookup tables for Z-scores. For example, if we want to find P(Z<1.96), we can use a Z-score table to find the cumulative probability associated with a Z-score of 1.96, which is approximately 0.975.
Therefore, P(Z<1.96) is approximately 0.975 or 97.5%.