For a normal distribution with mu equal to two and sigma equal to three, where does approximately 95% of the scores fall within?

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For a normal distribution with mu equal to two and sigma equal to three, where does approximately 95% of the scores fall within? 

Expert Solution
Step 1: Find the Z-scores for the 2.5th and 97.5th percentiles

Since the normal distribution is symmetric, you need to find the Z-scores that correspond to the lower and upper tails, each containing 2.5% of the total area under the curve. You can use a standard normal distribution table or a calculator to find these Z-scores.

For the 2.5th percentile (lower tail):

Z = Φ^(-1)(0.025) ≈ -1.96

For the 97.5th percentile (upper tail):

Z = Φ^(-1)(0.975) ≈ 1.96

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