Probability of Finding Defective Fuses in an Electronic System
What is the probability of finding no more than two defective fuses in the electronic system?
a. If the fuses are purchased and tested sequentially until the first defective fuse is observed, what is the probability that no more than two fuses are purchased and tested?
What are the mean, variance, and standard deviation for the number of fuses tested until the first defective fuse is observed?
b. Find the mean, variance, and standard deviation for X, the number of fuses tested until the first defective fuse is observed.
What is the probability of purchasing and testing five fuses until two defective fuses are observed?
c. What is the probability that five fuses are purchased and tested until two defective fuses are observed?
Probability of Finding No More Than Two Defective Fuses
a. The probability of finding the first defective fuse within two trials is 19%.
Mean, Variance, and Standard Deviation
b. The expected number of trials before finding a defective fuse is 10, with a variance of 90 and a standard deviation of about 9.49.
Probability of Purchasing and Testing Five Fuses
c. The probability of needing to test 5 fuses before finding 2 defective ones is approximately 7.29%.
The manufacturer uses electrical fuses in an electronic system and tests them sequentially until a certain number of defective fuses are observed. In this scenario, where the lot contains 10% defective fuses, various probabilities and statistics are calculated based on the testing process.
Probability of Finding No More Than Two Defective Fuses
From the properties of the geometric distribution, the probability of the first defective fuse occurring on the first or second trial is 10% + (90% * 10%) = 19%. This means that there is a 19% chance of finding no more than two defective fuses when testing sequentially.
Mean, Variance, and Standard Deviation
The mean, variance, and standard deviation for a geometric distribution can be calculated based on the probability of finding a defective fuse. In this case, the mean is 10 (the expected number of fuses that need to be tested before finding a defective one), the variance is 90, and the standard deviation is approximately 9.49.
Probability of Purchasing and Testing Five Fuses
In the scenario where five fuses are tested until two defective ones are found, a negative binomial distribution is applied. The probability that 5 fuses need to be tested until finding 2 defective ones is approximately 7.29%.
This calculation and analysis of probabilities and statistics in finding defective fuses in an electronic system provide valuable insights into the quality control process of the manufacturer and help in optimizing testing procedures for efficiency.