The total area under a standard normal curve is :
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Step-by-Step Solution
Step 1: Understand the Standard Normal Curve
The standard normal curve is a specific type of normal distribution with a mean of 0 and a standard deviation of 1. Its probability density function is given by the formula shown. This curve is symmetric around the mean.
Step 2: Interpret Area as Probability
In probability theory, the total area under the probability density function curve for any continuous random variable must equal 1. This represents the certainty that the random variable will take on some value within its entire range.
Step 3: State the Total Area
Since the standard normal curve is a probability distribution, the total area under its curve, from negative infinity to positive infinity, is always equal to 1. This is a fundamental property of all probability density functions.