Question

For a normally distributed population with a mean of 40 and a standard deviation of 5 find P(38 < X < 41). Give your answer rounded to 3 decimal places.

Answer 1

Given = 40, = 5

To find the probability, we need to find the z scores.

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P(38 < X < 41) = P(X < 41) - P(X < 38)

For P(X < 41) ; z = (41 - 40) / 5 = 0.2. The p value at this score is = 0.5793

For P(X < 38) ; z = (38 - 40) / 5 = -0.4. The p value at this score is = 0.3446

Therefore the required probability is 0.5793 – 0.3446 = 2347       0.235

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