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Probability Standard Normal

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Probability Standard Normal


1. The problem asks to find the probability \(P(0 < z < 2.65)\) using the standard normal distribution, where \(z\) is the standard normal variable. 2. Recall that the standard normal distribution is symmetric around zero, and the total area under the curve is 1. 3. \(P(0 < z < 2.65) = P(z < 2.65) - P(z < 0)\). 4. From the standard normal table or using software, \(P(z < 2.65) \approx 0.9960\). 5. Also, \(P(z < 0) = 0.5\) because zero is the mean. 6. Therefore, \(P(0 < z < 2.65) = 0.9960 - 0.5 = 0.4960\). 7. Converting to percentage, \(0.4960 = 49.60\%\). 8. Thus, the correct answer is \(\boxed{49.60\%}\).