Standard Normal DistributionA normally distributed random variable X is converted to a standard normal distribution (Z). What is the value of P(-1 < Z < 2)?47.5%68%81.5%95%
Question
Standard Normal DistributionA normally distributed random variable X is converted to a standard normal distribution (Z). What is the value of P(-1 < Z < 2)?47.5%68%81.5%95%
Solution
The value of P(-1 < Z < 2) in a standard normal distribution can be found by looking at the Z-table or using a standard normal distribution calculator.
Step 1: Identify the Z-scores. In this case, they are -1 and 2.
Step 2: Look up the corresponding probabilities for these Z-scores in the Z-table or use a standard normal distribution calculator. The probability for Z = -1 is 0.1587 (or 15.87%) and for Z = 2 is 0.9772 (or 97.72%).
Step 3: To find the probability that Z is between -1 and 2, subtract the probability of Z = -1 from the probability of Z = 2.
So, P(-1 < Z < 2) = P(Z = 2) - P(Z = -1) = 0.9772 - 0.1587 = 0.8185 or 81.85%.
Therefore, the correct answer is 81.5%.
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