For a standard normal distribution, what is the approximate probability that a randomly selected value lies between -1.5 and 1.5?
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Correct answer
B. 0.8664
Principle or equation
In a standard normal distribution, the empirical rule states that about 68% of data lies within 1 standard deviation, 95% within 2, and 99.7% within 3. For 1.5 standard deviations, the exact probability is approximately 0.8664.
Why this answer is correct
The probability that a standard normal random variable Z lies between -1.5 and 1.5 is P(-1.5 < Z < 1.5) = 2*Φ(1.5) - 1. Using standard normal tables, Φ(1.5) ≈ 0.9332, so the probability is 2*0.9332 - 1 = 0.8664.
Example
For Z between -1 and 1, the probability is about 0.6826, which is the 68% rule.
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