If the probability is 0.10 that a certain wide-flange column will fail under a g

Question

If the probability is 0.10 that a certain wide-flange column will fail under a given axial load, what are the probabilities that among 16 such columns a. At most two will fail? b. At least four will fail? If the probability is 0.20 that any person will dislike the taste of a new toothpaste, what is the probability that 5 of 18 randomly selected persons will dislike it? In the inspection of tin plates produced by a continuous electrolytic process. 0.2 imperfection is spotted on the average per minute. Find the probabilities of spotting a. One imperfection in 3 minutes b. At least two imperfections in 5 minutes

Explanation / Answer

Sol1:

Binomial distribution

n=16

p=0.1

q=1-p=1-0.1=0.9

sol1a:

P(X<=2)

=P(X=0)+P(X=1)+P(X=2)

=16C0(0.10)0(0.9)10-0 +10C1(0.10)1(0.9)10-9 +10C2(0.10)2 (0.9)10-2

=0.7892

Solution1b;

P(X>=4)

=P(X=4)+P(X=5)+P(X=6)+......P(X=16)

=0.0684

Solution2:

p=0.2

n=18

P(X=5) to be found

18C0(0.2)0 (1-0.2)18-0

=0.1507

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