a) The summer monsoon rains in India follow a normal distribution with mean `mu = 852` millimeters (mm) of rainfall and standard deviation `sigma = 82` mm. In the drought year 1987, `X = 697` mm of rain fell.The probability that the rainfall is less than or equal to 697 mm is calculated as follows:Since the distribution is normal, we have: `z = (X - mu)/sigma = (697 - 852)/82 = -1.89`Using a standard normal table, we find that the probability of a value less than or equal to -1.89 is `0.0294` or `2.94%`.Therefore, in `2.94%` of all years, India will have 697 mm or less of monsoon rain. (b) "Normal rainfall" means within `20` mm of the long-term average, or between `682` mm and `1022` mm. The probability that the rainfall is normal is calculated as follows:We have to find the probability that the rainfall is between `682` mm and `1022` mm. Since the distribution is normal, we have: `z_1 = (682 - 852)/82 = -2.07` and `z_2 = (1022 - 852)/82 = 2.07`Using a standard normal table, we find that the probability of a value less than or equal to -2.07 is `0.0196` and the probability of a value less than or equal to 2.07 is `0.9804`.Therefore, the probability that the rainfall is between `682` mm and `1022` mm is `0.9804 - 0.0196 = 0.9608` or `96.08%`.Therefore, in `96.08%` of all years, the rainfall is normal.