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Okay so to solve these we can use the principles of statistical process control, spc, and the specific characteristics of a fraction non -conforming control chart, so part a for the upper and lower control limits, well the process average is given as 0 .07, the sample size n is 400, and then for the control limits, so the upper control limit, the ucl, we take p plus 3 times the square root of p times 1 minus p over n, and then for the lower, it's just going to be minus, so for the lower control limit, it's the same thing here, but it's going to be p minus 3 times the square root of p times 1 minus p over n, and if the lcl is negative, we just set it to 0 as a non, as negative fractions non -conforming are not possible, so doing so we get here for part a that the upper control limit works out to be about 0 .1023, and the lower control limit works out to be 0 .0317, and then for, let's see, part b, so the probability of detecting a shift to 0 .10, so the process average is 0 .10, and then the standard deviation is the square root of p times 1 minus p over n, and then the z -score, well, there's the number of standard deviations, the new process average is from the old average, and then the probability, we just use the standard normal distribution to find the probability of observing a value as extreme as or more extreme than p prime equals 0 .10, and for part b, the probability then of detecting a shift here works out to be approximately 0 .93 percent, so that's 0 .0093, and then lastly for part c, this works out to be the same, the probability that this shift to 0 .10 will be detected on the first or second sample taken after this shift is also approximately 0 .0093, or again 0 .93 percent, and we can note these probabilities are quite low, indicating that there's a small chance of detecting the shift quickly with this control chart setup...