A packaging company has an old machine which improperly packages 30% of all its goods. The company has a special order to package 20 products for a client. Based on Chebyshev's theorem we can be 89% sure that between and of the products will be improperly packaged.

A packaging company has an old machine which improperly packages 30% of all its goods. The company has a special order to package 20 products for a client.

The probability that goods are improperly packaged is 0.30 and sample size is 20.

Then, μ = 20 x 0.30 =6

standard deviation, σ = √ [np(1-p)]

Put the values, we get

σ = 2.05

The value of k can be

1-1/k² = 0.89

Solving the expression for k, we get

k = 3.01

Based on Chebyshev's theorem, the limit are

μ ± kσ = (μ - kσ , μ + kσ )

={(6 - (3.01 x 2.05)) , (6 + (3.01 x 2.05)) }

={0,12}

Thus, we can be 89% sure that between 0 and 12 of the products will be improperly packaged.

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A packaging company has an old machine which improperly packages 30% of all its goods. The company has a special order to package 20 products for a client. Based on Chebyshev's theorem we can be 89% sure that between ____ and ____ of the products will be improperly packaged.

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A packaging company has an old machine which improperly packages 30% of all its goods. The company has a special order to package 20 products for a client. Based on Chebyshev's theorem we can be 89% sure that between and of the products will be improperly packaged.