A quality inspector picks a sample of 15 items at random from a manufacturing process known to produce 10% defective items. Let X be the number of defective items found in the random sample of 15 items. Assume that the condition of each item is independent of that of each of the other items in the sample. The probability distribution of X is provided in the excel file. Use simulation to generate 500 values of this random variable X. A) Use simulation to generate 500 values of this random variable X. B) Calculate the mean and standard deviation of the simulated values. How do they compare to the mean and standard deviation of the given probability distribution? Use excel to help please and attach... Previous writer did not include part A in excel Note: These probabilities were generated by a binomial distribution,. For now, you can just take these probabilities as given. Number of defective items in a random sample of 15 items # of defectives Probability 0 0.2059 1 0.3432 2 0.2669 3 0.1285 4 0.0428 5 0.0105 6 0.0019 7 0.0003 8 0.0000 9 0.0000 10 0.0000 11 0.0000 12 0.0000 13 0.0000 14 0.0000 15 0.0000

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Description: A quality inspector picks a sample of 15 items at random from a manufacturing process known to produce 10% defective items. Let X be the number of defective items found in the random sample of 15 items. Assume that the condition of each item is indep

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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A quality inspector picks a sample of 15 items at random from a manufacturing process known to produce 10% defective items. Let X be the number of defective items found in the random sample of 15 items. Assume that the condition of each item is independent of that of each of the other items in the sample. The probability distribution of X is provided in the excel file. Use simulation to generate 500 values of this random variable X.

A) Use simulation to generate 500 values of this random variable X.

B) Calculate the mean and standard deviation of the simulated values. How do they compare to the mean and standard deviation of the given probability distribution?

Use excel to help please and attach... Previous writer did not include part A in excel

Note: These probabilities were generated by a binomial distribution,. For now, you can just take these probabilities as given.

Number of defective items in a random sample of 15 items

# of defectives	Probability
0	0.2059
1	0.3432
2	0.2669
3	0.1285
4	0.0428
5	0.0105
6	0.0019
7	0.0003
8	0.0000
9	0.0000
10	0.0000
11	0.0000
12	0.0000
13	0.0000
14	0.0000
15	0.0000

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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A) Use simulation to generate 500 values of this random variable X.B) Calculate the mean and standard deviation of the simulated values. How do they compare to the mean and standard deviation of the given probability distribution?

A) Use simulation to generate 500 values of this random variable X.

B) Calculate the mean and standard deviation of the simulated values. How do they compare to the mean and standard deviation of the given probability distribution?