Probability Between Two ZScores

Find the probability that Z is between -0.21 and 0.85.

When dealing with problems related to the standard normal distribution, it's essential to understand the properties of the standard normal curve. This curve is symmetrical and centered around a mean of zero with a standard deviation of one. The problem here asks you to determine the probability of a standard normal random variable (commonly denoted as Z) falling between two given values. This is quite common in statistical analysis, especially when standardizing values to understand how they relate to a mean.

To solve this problem, you generally use a Z-table or computational tools like statistical software. A Z-table provides the area under the curve to the left of a given Z-score. To find the probability of Z being between two values, you calculate the cumulative probability for the upper Z value and subtract the cumulative probability for the lower Z value. This area between the two scores represents the probability you're looking for. This type of analysis is fundamental for making inferences about population parameters, especially when it comes to hypothesis testing and confidence intervals, where you often need to understand the likelihood of sample results under the normal distribution.