Question

In: Statistics and Probability

3. Historically, a textile company samples three sheets of a certain material as part of incoming...

3. Historically, a textile company samples three sheets of a certain material as part of incoming inspection and the historical 10.5 blemishes are found on average. If a sample of one sheet of this material is tested, based on the Poisson distribution:

a) How many blemishes should be found on average in this sample?

b) What is the probability that 4 or more blemishes will be found?

Expert Solution

X : Number of blemishes will be found in a sample of one sheet

Given,

Historical 10.5 blemishes are found on average in samples of three sheets of a certain material as part of incoming inspection

Therefore,

a) Number blemishes should be found on average in this sample of one sheet = 10.5/3 = 3.5

X follows Poisson distribution with mean : = 3.5

Probability mass function of a Poisson distribution

i.e

Probability that 'x' blemishes will be found is given by

b) Probability that 4 or more blemishes will be found = P(X4) = 1 - [P(X=0)+P(X=1)+P(X=2)+P(X=3)]

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.03020+0.10569+0.18496+0.21579= 0.53664

P(X4) = 1 - [P(X=0)+P(X=1)+P(X=2)+P(X=3)] = 1-0.53664 = 0.46336

Probability that 4 or more blemishes will be found = 0.46336

orchestra answered 2 years ago

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