5. (10%) Suppose out of the 250,000 people who came to Taiwan in the first half of 2021, 500 people were COVID-19 carriers. The PCR tests are able to correctly identify the COVID-19 carriers 90 out 100 times on average. On the other hand, PCR tests will show positive results for the non-carriers 5% of the times. How many false positives and false negatives are expected to be identified from the 250,000 people who entered Taiwan? Explain why CDC decided to impose the quarantine (isolation) measures on passengers from abroad even though they had been tested negative for the PCR tests back in 2021?

6. (20%) A manufacturing company produces electrical switches. To test the strength of the switches, robustness testing is carried out on 100 switches to determine how many times before the switch breaks down. The average of number of uses is 1.245 million times and the standard deviation is 0.3 million. The company would like to investigate whether or not the population mean of usage is more than 1.2 million times.A. At the 0.10 level of significance, is there evidence that the population mean of the number of usage is more than 1.2 million? Please form the null hypothesis and alternative hypothesis respectively before performing statistical tests.B. When the true population mean is 1.240 million and the level of significance is set as 0.05, what is the probability of making type I and type II errors respectively?Square root of numbers:

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