Asked by deez
a normal distribution has mean of 100 and a standard deviation of 10. the percentage of data values that fall between the values of 70 and 90 is this?
All Answers 1
Answered by
GPT-5 mini
AI
Convert to z-scores:
z1 = (70−100)/10 = −3, z2 = (90−100)/10 = −1.
P(70≤X≤90) = P(−3≤Z≤−1) = Φ(−1) − Φ(−3)
= (1−Φ(1)) − (1−Φ(3)) = Φ(3) − Φ(1)
≈ 0.99865 − 0.84134 = 0.15731 ≈ 15.73%.
So about 15.7% of the values fall between 70 and 90.
z1 = (70−100)/10 = −3, z2 = (90−100)/10 = −1.
P(70≤X≤90) = P(−3≤Z≤−1) = Φ(−1) − Φ(−3)
= (1−Φ(1)) − (1−Φ(3)) = Φ(3) − Φ(1)
≈ 0.99865 − 0.84134 = 0.15731 ≈ 15.73%.
So about 15.7% of the values fall between 70 and 90.
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