MathsGee Answers is Zero-Rated (You do not need data to access) on: Telkom | Dimension Data | Rain | MWEB
First time here? Checkout the FAQs!
MathsGee is Zero-Rated (You do not need data to access) on: Telkom |Dimension Data | Rain | MWEB

0 like 0 dislike
Suppose that $0.3 \%$ of bolts made by a machine are defective, the defectives occurring at random during production. If the bolts are packaged in boxes of 100 , what is the Poisson approximation that a given box will contain $x$ defectives? Suppose you buy 8 boxes of bolts. What is the distribution of the number of boxes with no defective bolts? What is the expected number of boxes with no defective bolts?
in Data Science & Statistics by Diamond (74,866 points) | 22 views

1 Answer

0 like 0 dislike
Best answer
$D$ is $\operatorname{Bin}(100,0.003)$ which is approximately Poisson with parameter $100 \times 0.003=0.3 .$ Hence $P(D=$ $x) \approx e^{-0.3}(0.3)^{x} / x !, x=0,1, \ldots$ In particular, $P(D=0) \approx 0.7408 .$ Finally, $N$, the no. of boxes with no defectives is $\operatorname{Bin}(8,0.7408)$ and so $E(N)=8 \times 0.7408=5.926$.
by Diamond (74,866 points)

Related questions

MathsGee provides answers to subject-specific educational questions for improved outcomes.

On MathsGee Answers, you can:

1. Ask questions
2. Answer questions
3. Comment on Answers
4. Vote on Questions and Answers
5. Donate to your favourite users

MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

ZeroEd Search Engine

Other Tools

MathsGee ZOOM | eBook