A researcher is studying the age of senior citizens in a region. She randomly selects a sample of 50 senior citizens from the entire population, which is approximately normally distributed, with a mean of 80 years and a standard deviation of 10 years. a. What is the probability that the senior citizens' age is at most 85 years? b. What is the probability that the senior citizens' age is not more than 75 years? c. Find the bottom 20% of the senior citizens' age. d. Determine an interval, which is symmetrically distributed around the population mean, that will include 90% of the sample mean. *****I need help in a and b specifically - Step by step solution Here are the answers (a) The probability that a senior citizen's age is at most 85 years is 0.9738. (b) The probability that a senior citizen's age is not more than 75 years is 0.00023. (c) The age of the bottom 20% of the senior citizens is approximately 79 years. (d) The interval that is symmetrically distributed around the population mean, which will include 90% of the sample mean is 77.6736 and 82.3264.