For a standard normal distribution, what is the approximate probability that a randomly selected value lies between -2 and 1?
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Correct answer
A. 0.8185
Principle or equation
The standard normal distribution has mean 0 and standard deviation 1. The probability that Z lies between a and b is Phi(b) - Phi(a), where Phi is the cumulative distribution function. Use the empirical rule or standard normal table: Phi(1) ≈ 0.8413, Phi(-2) ≈ 0.0228.
Why this answer is correct
We need P(-2 < Z < 1) = Phi(1) - Phi(-2). From the standard normal table, Phi(1) = 0.8413 and Phi(-2) = 0.0228. The difference is 0.8413 - 0.0228 = 0.8185.
Example
For Z ~ N(0,1), P(-1 < Z < 1) = Phi(1) - Phi(-1) = 0.8413 - 0.1587 = 0.6826.
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