Question

1. Dolomite is a common rock-forming mineral and the primary component of the sedimentary rock. During mining operations, dolomite is often mixed up with shale, which is another fine-grained sedimentary rock. Miners can make use of the radioactivity features of rock to help them distinguish between shale rock zone and dolomite rock zone. Based on certain guidelines and standards, if the gamma ray reading of a rock zone is less than 70 API units, the area is considered to be abundant in dolomite, and hence can be mined. On the other hand, if the gamma ray reading of a rock zone exceeds 70 API units, then the area is considered to be mostly shale and therefore will not be mined. In an exploratory research study, a random set of 750 sample data is collected from a rock quarry. It is found that 480 of the samples are dolomite and 270 of the samples are shale. Of the 480 dolomite samples, 50 of them had gamma rays readings greater than 70. As for the 270 share samples, 255 of them had gamma ray readings greater than 70. Suppose a gamma ray reading greater than 70 is obtained at a particular depth of the rock quarry. Compute the probability that the area should be mined.

Answer 1

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