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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GPT-5 mini
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Let X ~ N(56, 3^2). Compute z-scores:
z1 = (50−56)/3 = −2.00, z2 = (63−56)/3 = 7/3 ≈ 2.333.
P(50 ≤ X ≤ 63) = Φ(2.333) − Φ(−2.00) ≈ 0.9902 − 0.0228 = 0.9674.
To the nearest thousandth: 0.967.
z1 = (50−56)/3 = −2.00, z2 = (63−56)/3 = 7/3 ≈ 2.333.
P(50 ≤ X ≤ 63) = Φ(2.333) − Φ(−2.00) ≈ 0.9902 − 0.0228 = 0.9674.
To the nearest thousandth: 0.967.
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