GATE 2018 CE (CE1) – Question 28
Twenty concrete cubes have compressive-strength frequencies (MPa; count): (23;4), (28;2), (22.5;5), (31;5), (29;4). For mean μ and standard deviation σ, how many specimens have strength below $\mu-3\sigma$?
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Correct answer: 0 to 0
Explanation
The weighted mean is $\mu=[23(4)+28(2)+22.5(5)+31(5)+29(4)]/20=26.575$ MPa. The population standard deviation is about 3.59 MPa, putting $\mu-3\sigma$ near 15.81 MPa, below the minimum 22.5 MPa. Hence no specimens qualify: 0. Using the sample standard deviation gives the same count.