The mid-day wind speed, in knots, at a coastal resort is normally distributed with mean 12.8 and standard deviation σ.

a. Given that 15% of the recorded wind speeds are less than 10 knots, find the value of σ.

b. Calculate the probability that exactly two out of 10 randomly selected recordings are less than 10 knots.

c. Using a suitable approximation, calculate an estimate of the probability that at least 13 out of 100 randomly selected recordings are over 15.5 knots.