Standardize a normal interval, calculate probabilities and determine a lower quantile.

Reaction times of human beings are normally distributed with a mean of 0.76 seconds and a standard deviation of 0.06 seconds.

1. The graph below is that of the standard normal curve. The shaded area represents the probability that the reaction time of a person chosen at random is between 0.70 and 0.79 seconds.[6]
   1. Write down the value of a and of b.
   2. Calculate the probability that the reaction time of a person chosen at random is (a) greater than 0.70 seconds and (b) between 0.70 and 0.79 seconds.
2. Three percent (3%) of the population have a reaction time less than \(c\) seconds.[4]
   1. Represent this information on a diagram similar to the one above. Indicate clearly the area representing 3%.
   2. Find c.