(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 binomial distribution to answer the question
(c)
The records show that 8% of the items produced by a machine do not meet the specifications. Use the normal approximation to the binomial distribution to answer the following questions. What is the probability that a sample of 100 units contains. What is the probability that this sample of 100 units contains ten or fewer defective units? Use the normal approximation to the binomial distribution to answer the question.
a) The standard deviation here is computed as:
b) The number of defective parts out of 100 could be modelled here as:
This can be approximated to a normal distribution as:
The required probability here is computed as:
Applying the continuity correction, we get here:
Converting this to a standard normal variable, we get:
Getting it from the standard normal tables, we get:
Therefore 0.9015 is the required probability here.
c) The required probability here is computed as:
P( X <= 10 )
Applying the continuity correction, we get here:
P(X < 10.5 )
Converting this to a standard normal variable, we get:
Getting it from the standard normal tables, we get:
Therefore 0.8216 is the required probability here.
(a) The records show that 8% of the items produced by a machine do not meet...
Suppose a lot of 10,000 items has 200 defective items and that a random sample of 30 is drawn from the lot. What is the probability (to four decimal places) of getting exactly 1 defective in the sample? Do not use Poisson or binomial approximation.
The probability that a part produced by a certain factory's assembly line will be defective is 0.025. Suppose a sample of 130 parts is taken. Find the following probabilities by using the normal curve approximation to the binomial distribution. Use the table of areas under the standard normal curve given below. The probability that exactly 2 parts will be defective is ____. (Round to four decimal places as needed.) The probability that no parts will be defective is _____. (Round...
Suppose that 25 percent of the items produced by a certain machine are defective and the parts are independent of each other. We will sample n items at random and inspect them. What is the expected value and variance for the described distribution?
3. A manufacturer knows that, on average, 3% of items manufactured will have defects. Use the normal approximation to the binomial distribution to determine the probability that among 200 items, (a) at the most 5 will be defective; (b) anywhere from 4 to 7 will be defective 4. Page 140, #5.26 5. Page 178 #5.109
You may need to use the appropriate appendix table or technology to answer this question. Although studies continue to show smoking leads to significant health problems, 30% of adults in a country smoke. Consider a group of 250 adults. (b) What is the probability that fewer than 65 smoke? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) (c) What is the probability that from 80 to 85 smoke? Use...
When a particular machine is functioning properly, 75% of the items produced are non-defective. If eight items are examined, what is the probability that one is defective? If eight items are examined, what is the probability that exactly three are non-defective? If eight items are examined, what is the probability that at least 6 are non-defective?
When a particular machine is functioning properly, 80% of the items produced are non-defective. If 3 items are examined, what is the probability that one is defective?
Assume that a factory has two machines ??A_1 and ??A_2 . Past records shows that machine ??A_1 produces 60% of the items of output and machine ??A_2 produces 40% of the items. Further, 2% of the items produced by machine ??A_1 were defective and only 1% produced by machine ??A_2 were defective. If a detective item is drawn at random, what is the probability that it was produced by machine ??A_1 ?
Use the normal approximation to the binomial distribution to answer this question and save your answer up to 4 decimal points. Suppose that twenty percent of students who finish high school do not go to college. Now consider a sample of 100 high school students, the probability that fourteen or fewer will not go to college is [__].
process for manufacturing an electronic com- nt yields items of which 190 are defective. A qual- ity control plan is to select 100 items from the process, and if none are defective, the process continues. Use the normal approximation to the binomial to find (a) the probability that the process continues given the sampling plan described; (b) the probability that the process continues even if the process has gone bad (i.e., if the frequency of defective components has shifted to...