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01-08-2020
Mathematics

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The mean of normally distributed test scores is 82 and the standard deviation is 5. If there are 241 test scores in the data sample, how many of them were in the 92 to 97 range?

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01-08-2020

Answer:

5

Step-by-step explanation:

Find the z-scores.

z = (x − μ) / σ

z₁ = (92 − 82) / 5

z₁ = 2

z₁ = (97 − 82) / 5

z₂ = 3

Find the probability:

P(92 < X < 97)

P(2 < Z < 3)

P(Z < 3) − P(Z < 2)

0.9987 − 0.9772

0.0215

Find the number of tests:

0.0215 (241) ≈ 5

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