If a random variable has a normal distribution with mean 80 and standard deviation 20

If a random variable has a normal distribution with mean 80 and standard deviation 20. what is the probability that it assumes the following values? a) Less than 77.4 b) Between 61.4 and 72.9 c) Greater than 90.0 d) Less than 67.6 or greater than 88.8 e) Between 92.1 and 95.4 f) Between 75.0 and 84.2 g) Exactly 81.7 2. Problem 2 Four samples are taken and averaged every hour from a production line and the hourly measurement of a particular impurity is recorded. Approximately one out of six of these averages exceeds 1.5% when the mean value is approximately 1.4%. State assumptions that would enable you to determine the proportion of the individual readings exceeding 1.6%. Make the assumptions and do the calculations. Are these assumptions likely to be true? If not, how might they be violated? ________________________________________