you work as a procurement engineer in a company that produces electronic device; your manager asked you to measure a sample of 50 resistors from a batch, which the supplier claims that are all 10KΩ. The data measured is displayed in a frequency distribution as follows: Resistance (R) KΩ frequency 9.6 ≤ R ≤ 9.7 1 9.7 ≤ R ≤ 9.8 2 9.8 ≤ R ≤ 9.9 5 9.9 ≤ R ≤ 10 17 10.0 ≤ R ≤ 10.1 18 10.1 ≤ R ≤ 10.2 5 10.2 ≤ R ≤ 10.3 1 10.3 ≤ R ≤ 10.4 1 After making the measurements, you manager asked you to perform several tasks: 1. Calculate the mean and standard deviation of the measured data. 2. Draw a histogram and a frequency polygon for this data. 3. Based on what you found in 1 & 2, write down a paragraph consisting of 4-5 lines maximum, explaining this statistical data to a customer who has no technical background. Do not expect the customer to understand what terms like mean, standard deviation, frequency polygon and histogram mean. 4. Assuming that the distribution of resistance is normal, find the probability that: i. A randomly chosen resistor will be greater than 10.1 KΩ. ii. A randomly chosen resistor will be greater than 9.5 KΩ and smaller than 10.3KΩ. 5. The supplier claims that the mean resistance for all purchased resistors is equal to10 KΩ; using the data and measurements which you have made on 50 resistors test this hypothesis. 6. Your manager has asked you to summarize the statistical data you have been investigating in a method that can be understood by your non-technical colleagues in the procurement department, you are required to present all this information to them in a short meaningful report.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
you work as a procurement engineer in a company that produces electronic device; your manager asked you to measure a sample of 50 resistors from a batch, which the supplier claims that are all 10KΩ. The data measured is displayed in a frequency distribution as follows:
Resistance (R) KΩ frequency 9.6 ≤ R ≤ 9.7 1 9.7 ≤ R ≤ 9.8 2 9.8 ≤ R ≤ 9.9 5 9.9 ≤ R ≤ 10 17 10.0 ≤ R ≤ 10.1 18 10.1 ≤ R ≤ 10.2 5 10.2 ≤ R ≤ 10.3 1 10.3 ≤ R ≤ 10.4 1
After making the measurements, you manager asked you to perform several tasks: 1. Calculate the
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