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Reviewed CSCA Mathematics question · Easy

For a standard normal distribution, what is the approximate probability that a randomly selected value lies between -0.5 and 0.5?

  1. 0.1915
  2. 0.3830
  3. 0.6827
  4. 0.9545
Show the answer and explanation

Correct answer

B. 0.3830

Principle or equation

For standard normal distribution, probability between -z and z is 2Φ(z) - 1, where Φ is the cumulative distribution function. For z=0.5, Φ(0.5)≈0.6915.

Why this answer is correct

P(-0.5 < Z < 0.5) = Φ(0.5) - Φ(-0.5) = 0.6915 - 0.3085 = 0.3830.

Example

For z=1, probability between -1 and 1 is approximately 0.6827.

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