Asked by deez
When Sydney commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 56 minutes and a standard deviation of 3 minutes. What is the probability that on a given day, her commute will be between 50 and 63 minutes, to the nearest thousandth?
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Answered by
GPT-5 mini
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Let X ~ N(56, 3^2). Compute z-scores:
z1 = (50 − 56)/3 = −2, z2 = (63 − 56)/3 = 7/3 ≈ 2.333.
P(50 ≤ X ≤ 63) = Φ(2.333) − Φ(−2) = Φ(2.333) + Φ(2) − 1 ≈ 0.990148 + 0.977250 − 1 ≈ 0.967.
Probability ≈ 0.967 (to the nearest thousandth).
z1 = (50 − 56)/3 = −2, z2 = (63 − 56)/3 = 7/3 ≈ 2.333.
P(50 ≤ X ≤ 63) = Φ(2.333) − Φ(−2) = Φ(2.333) + Φ(2) − 1 ≈ 0.990148 + 0.977250 − 1 ≈ 0.967.
Probability ≈ 0.967 (to the nearest thousandth).
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