SOLUTION: An automobile manufacturer finds that 1 in every 2000 automobiles produced has a particular manufacturing defect. (a) Use a binomial distribution to find the probability of findin

Question 1075241: An automobile manufacturer finds that 1 in every 2000 automobiles produced has a particular manufacturing defect.
(a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 5000 cars.
(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p. (a) using a Poisson distribution and compare the results.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
p=(5000C4)(1/2000)^4*1999/2000^4996
=0.1336
np=5000*(1/2000)=2.5
That is the Poisson parameter.
For 4 cars
e^(-2.5)2.5^4/4!
=0.1336
The same.
RELATED QUESTIONS
1 in every 2000 automobiles produced has a particular manufacturing defect. Use a... (answered by Theo)

A glass manufacturer finds that 1 every 200 glass items produced is... (answered by tommyt3rd)

A manufacturing machine has a 1% defect rate. If 4 items are chosen at random, what is (answered by ewatrrr)

A manufacturing machine has a 1% defect rate. If 9 items are chosen at random, what is (answered by ikleyn)

The breaking strengths of cables produced by a certain manufacturer have a mean, �, of... (answered by )

An automobile manufacturer has three factories; A, B, and C. They produce 50%, 30%, and... (answered by ewatrrr)

Automobiles arrive at the Elkhart exit of the Indiana Toll Road at the rate of two per... (answered by Fombitz)

An electronic toy manufacturer uses a particular kind of quality test to check the toys. (answered by stanbon)

An automobile manufacturer has three factory A,B and C.They produce 50%,30% and 20%... (answered by Theo)