(a) In a manufacturing process, the diameter of steel rods is distributed normally with a mean value of 5 mm and standard deviation of 0.1 mm. If a rod is selected at random, what is the probability that its diameter will be: (i) less than 4.85 mm; (ii) between 4.9 mm and 5.1 mm? (b) A telephone exchange receives an average of 5 calls per minute. Calculate the probability that, in a given minute, the exchange receives: (i) exactly 5 calls; (ii) 2 calls or fewer

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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(a) In a manufacturing process, the diameter of steel rods is distributed normally with a mean value of 5 mm and standard deviation of 0.1 mm. If a rod is selected at random, what is the probability that its diameter will be:

(i) less than 4.85 mm;

(ii) between 4.9 mm and 5.1 mm?

(b) A telephone exchange receives an average of 5 calls per minute. Calculate the probability that, in a given minute, the exchange receives:

(i) exactly 5 calls;

(ii) 2 calls or fewer.

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