Normal Probability of Cylinder Strength
Mediumnormal distributionprobability
Concrete cylinder strengths are normally distributed with mean 50 MPa and standard deviation 5 MPa. The probability that a cylinder exceeds 60 MPa is most nearly:
- A0.0455
- B0.0228
- C0.1587
- D0.9772
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Answer: B. 0.0228
Equation: z = (x − μ)/σ; P(X > x) = 1 − Φ(z). Values: μ = 50 MPa, σ = 5 MPa, x = 60 MPa. Step 1: z = (60 − 50)/5 = 2.0. Step 2: Φ(2.0) = 0.9772 from the standard normal table. Step 3: P = 1 − 0.9772 = 0.0228. 0.1587 uses z = 1; 0.9772 is the area to the left; 0.0455 is the two-tailed probability.
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