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Let Z be a standard normal random variable. a. Find P(Z > 0).

User LemonMan
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Final answer:

In a standard normal distribution, the probability P(Z > 0) is 0.5 since the distribution is symmetric and half the values lie above the mean.

Step-by-step explanation:

The standard normal distribution Z~N(0, 1) means that the mean (μ) is 0 and the standard deviation (σ) is 1. The probability P(Z > 0) represents the area under the normal curve to the right of the mean. Since the total area under the curve is 1 and the curve is symmetric around the mean, P(Z > 0) is equal to 0.5. This is because exactly half of the values lie above the mean and half below in a standard normal distribution. This probability does not require looking up a z-table as it is a fundamental property of the symmetric normal distribution.

User Walty Yeung
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