The reading given by a thermometer calibrated in ice water (actual temperature 0°c) is a random variable with probability density function where k is a constant.

f(x) = k(1 - x^2) for -1 < x < 1
f(x) = 0 for otherwise

(a) find the value of k.
(b) what is the probability that the thermometer reads above 0°c?
(c) what is the probability that the reading is within 0.25°c of the actual temperature?
(d) what is the mean reading? what is the median reading? what is the standard deviation?