3. (10%) In American football, teams take turns in offense and defense. Assume that the only way teams can score is through offense. In the overtime, the team that scores first wins the game and they keep playing until a winner comes through. There is no tie game. Suppose Team A takes the offense first against Team B, and the probability of scoring at offense is 50% for either of the teams. What is the winning probability for Team A when they play in the overtime? What is the winning probability of Team B?

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:| Number | 10 | 20 | 30 | 40 | 50 | 60 || --- | --- | --- | --- | --- | --- | --- || SQRT | 3.16 | 4.47 | 5.48 | 6.32 | 7.07 | 7.75 |

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