a) Let X = number of nonconforming items produced in a particular process
p = 0.05 = probability of nonconforming items produced in a process
n = sample size = 40
So X follows binomial distribution with parameters n = 40 and p = 0.05
b) Here we want to find P( X <= 3)
Let's use excel:
P( X <= 3) = "=BINOMDIST(3,40,0.05,1)" = 0.8619
c) Let = n*p = 40*0.05 = 2
Therefore X follows approximately Poisson distribution with parameter = 2
Let's use excel to find P( X <= 3)
P( X <= 3) = "=POISSON(3,2,1)" = 0.8571
d) From part a) and b) the difference is = 0.8619 - 0.8571 = 0.0047 which is very small.
Because for large n and very small p ; we can use Poisson approximation to the Binomial.
And here n = 40 , p = 0.05
that is both the conditions are satisfied. So we get good approximated probability when we use Poisson distribution.
please help ... 4-22) A process is known to produce 5% nonconforming items. A sample of...
In a lot of 200 electrical fuses, 20 are known to be nonconforming. A sample of 10 fuses is selected.(a) What is the probability distribution of the number of nonconforming fuses in the sample? What are its mean and standard deviation?(b) Using the binomial distribution as an approximation to the hypergeometric, find the probability of getting 2 nonconforming fuses. What is the probability of getting at most 2 nonconforming fuses?
please help ... 4-24 In a lot of 200 electrical fuses, 20 are known to be nonconforming. A sample of 10 (a) What is the probability distribution of the number of nonconforming fuses in the (b) Using the binomial distribution as an approximation to the hypergeometric, find fuses is selected. sample? What are its mean and standard deviation? the probability of getting 2 nonconforming fuses. What is the probability of getting at most 2 nonconforming fuses?
(1 point) Klinefelter syndrome, alternatively known as XXY, is a genetic disorder characterised by the presence of an extra X chromosome. The disorder only affects males. Suppose a researcher estimates that the probability that a newborn male will have Klinefelter syndrome is 0.0014. Suppose that a particular hospital delivers 1797 male babies in a year. Part a) Using a binomial model, what is the probability that more than two of the male births have Klinefelter syndrome? Give your answer to...
A manufacturing process produces semiconductor chips with a known failure rate of 5.3%. If a random sample of 275 chips are selected, approximately the probability that more than 13 will be defective. Use the normal approximation to the binomial with a correction for continua tee
(3 points) Klinefelter syndrome, alternatively known as XXY, is a genetic disorder characterised by the presence of an extra X chromosome. The disorder only affects males. Suppose a researcher estimates that the probability that a newborn male will have Klinefelter syndrome is 0.0017. Suppose that a particular hospital delivers 1262 male babies in a year. Part a) Using a binomial model, what is the probability that more than two of the male births have Klinefelter syndrome? Give your answer to...
(a) The records show that 8% of the items produced by a machine do not meet the specifications. You take a sample of 100 units. Find the standard deviation (Use exactly two decimal places) (b) The records show that 8% of the items produced by a machine do not meet the specifications. You take a sample of 100 units. What is the probability that this sample of 100 units contains five or more defective units?Use the normal approximation to the...
*************[[[[[[[[[[[[[[Solve parts a,b and c using Poissons distribution as an approximation of Binomial distribution]]]]]]]]]]]]]]************* Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X denote the number of parts in the sample of 20 that require rework. A process problem is suspected if X exceeds its mean by more than 3 standard deviations. (a) If the percentage of parts that require rework remains at 1%, what is the...
According to a census, approximately 5% of the population earned between $75,000 and 100,000 annually in 2008. A random sample of 30 people in the population was selected. a. Use the binomial distribution to determine the probability that fewer than three individuals earned between 75,000 and 100,000 annually in 2008. b. Use the Poisson approximation to the binomial distribution to determine the probability that fewer than three individuals earned between 75,000 and 100,000 annually in 2008. c. How do these...
1. One way of exposing under-coverage, non-response and other sources of error in sample surveys is to compare the results with known facts about the population. According to the 2010 US Census, about 1.6% of the population of the USA is Native American so the number of Native Americans in large random samples should vary approximately Normally. (a, b) What are the criteria for assessing whether a binomial sample can be approximated by a Normal distribution? (c) Based on those...
2) The Poisson distribution is a good approximation to the binomial when n is large, p is small, and the Poisson parameter λ is set equal to np. You can do this problem with paper, pencil, and a calculator. Report answers to parts a) and b) to four decimal places a) Suppose that a disease affects approximately one out of 10,000 people. Assuming independence of people getting the disease, what is the probability that ina population of 100,000 people, there...