In designing an electrical circuit, a probability density function is needed to be integrated to determine the confidence interval. For an oscillator to have its frequency within 5% of the target of 1 kHz, the likelihood of this happening can then be determined by finding the total area under the normal distribution for the range in question. This is given in the form: x2 1 exp 2 dx f(x) = Use a 3rd order Romberg's integration to find this frequency with xo = -1.751 and x= 3.989.