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2 Part Question Part 2 Probability

Statistics
Tutor: None Selected Time limit: 0 Hours

A man has designed a machine to produce a compound and  has calibrated it so the compound always has an atomic weight of 20.4. Unbeknownst to him, the machine has a defect and doesn't always produce a compound with that weight. Assume that the distribution of the weights of the compounds produced by the machine is normal with a mean of 21.37 and standard deviation of 0.4

Suppose 15 compounds are selected independently. What is the P that at most 2 of the compounds have a weight less than 20.857?

Apr 25th, 2015

Z = 20.857 - 21.37 / 0.4 = -1.28

P(Z < -1.28) = 0.1

15C2(0.1)^2(0.9)^13 = 0.2669

15C1(0.1)^1(0.9)^14 = 0.3432

15C0(0.1)^0(0.9)^15 = 0.2059

0.2669 + 0.3432 + 0.2059 = 0.816

Apr 25th, 2015

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