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 considers that their mean value is 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: 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 considers that the mean resistance for all purchased resistors is equal to 10 KΩ; using the data and measurements which you have made on 50 resistors, you have provided a new claim that the mean is not equal to 10 KΩ, test this hypothesis; select an appropriate test and conduct it using two different level of significance a =0.05 and 0.01, interpret the results in both cases
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
. 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 considers that their
value
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:
4. Assuming that the distribution of resistance is normal, find the
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 considers that the mean resistance for all purchased resistors is equal to 10 KΩ;
using the data and measurements which you have made on 50 resistors, you have provided a
new claim that the mean is not equal to 10 KΩ, test this hypothesis; select an appropriate test
and conduct it using two different level of significance a =0.05 and 0.01, interpret the results
in both cases
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