2. Computer chips have pins to connect them into sockets on computer boards. The thickness of the pins is important in determining the quality of the connection to the board. When the production process is running properly, the mean diameter of pins (relative to the deign specification) is 1.000. There is some inevitable variation in diameters as they are normally distributed, with the standard deviation being 0.006 unit. A pin will make a highest-quality connection only if its diameter is between 0.997 and 1.003 units. What is the probability that an individual pin will make such a connection? Show all work. (10 points)

3.. Related to Problem #2, as part of its ongoing quality monitoring, the chip manufacturer takes samples of 20 pins from each lot of 25,000 pins. Assuming that the process is running properly, what is the probability that the mean diameter in the sample will be between 0.997 and 1.003 units? Show all work. (10 points)

4. Related to Problem #3, instead of samples of 20 from each lot of 25,000 pins, the manufacturer takes samples of 10 pins from each lot of 25,000 pins to make the sampling process more efficient. Would you expect the probability that the mean diameter in the sample will be between 0.997 and 1.003 units? Why or Why not? – answer by (a) a qualitative explanation and (b) by quantitative explanation by calculating the probability. (10 points)

5. Similar to the setting related to Problem #4, the data (age in days) from the 33 stores showed the sample mean to be 56.869 days, and the sample standard deviation to be 28.97, which well represented the population standard deviation. At a sample size of 100, what is the margin of error for confidence interval of 99%? Show all work. (10 points)

6. Similar to the setting related to Problem #4, the data (age in days) from the 33 stores showed the sample mean to be 56.869 days, and the sample standard deviation to be 28.97, which could be counted on as population standard deviation. Using a sample size that is smaller – that is 50 – determine the confidence interval using 90% confidence level. Show all work. (10 points)

7. State what the interval determined in Problem #6 means. (5 points)