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Given a standard normal distribution, what is the area to the left of ? (Round your answer to 4 decimal places.)
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6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
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For the standard normal probability distribution, the area to the left of the is:
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Recall that the standard normal distribution is symmetric about its mean, which is 0.
Understand that the total area under the standard normal curve is 1, representing the total probability.
Since the distribution is symmetric, the area to the left of the mean (0) is exactly half of the total area.
Express this mathematically as the probability \(P(Z < 0) = 0.5\), where \(Z\) is a standard normal random variable.
Therefore, the area to the left of the mean in a standard normal distribution is 0.5.
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