To determine Whether the area should be mined or not if the obtained gamma ray reading is greater than 60 at a certain depth of the rock quarry. Explanation Given info: If the gamma ray reading of a rock zone exceeds 60 API units, the area is considered to be mostly shale, if the gamma ray reading of a rock zone is less than 60 API units, the area is considered to be abundant in dolomite. A random sample of 771 cores is taken and 476 of the samples dolomite, 295 were shale. Of the 476 dolomite core samples, 34 had a gamma ray reading greater than 60. Of the 295 core samples, 280 had a gamma ray reading greater than 60. Calculation: Define the following events: S : { Shale } D : { Dolomite } G : { Gamma ray reading > 60 } The probability values for the events are: P ( D ) = 476 771 = 0.617 P ( S ) = 295 771 = 0.383 P ( G | D ) = 34 476 = 0.071 P ( G | S ) = 280 295 = 0.949 The probability of the event D ∩ G is obtained as, P ( D ∩ G ) = P ( G | D ) P ( D ) Substitute, P ( G | D ) = 0.071 and P ( D ) = 0.617 in the above equation. Then, P ( D ∩ G ) = P ( G | D ) P ( D ) = ( 0.071 ) ( 0.617 ) = 0.0438 The probability of the event G is, P ( G ) = P ( G | D ) P ( D ) + P ( G | S ) P ( S )

13th Edition

ISBN: 9780134080215

Author: James T. McClave, Terry T Sincich

Publisher: PEARSON

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Chapter 3.8, Problem 143ACI

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Whether the area should be mined or not if the obtained gamma ray reading is greater than 60 at a certain depth of the rock quarry.

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Chapter 3.8, Problem 142ACI

Chapter 3.8, Problem 144ACI

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Statistics (13th Edition)

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