The standard normal probability function can be approximated as $$$F\left( {{X_N}} \right) = {1 \over {1 + \exp \left( { - 1.7255{X_N}{{\left| {{X_N}} \right|}^{0.12}}} \right)}}\,\,\,$$$
$$\,{X_N} = $$ standard normal deviate. If mean and standard deviation of annual precipitation are $$102$$ cm and $$27$$ cm respectively, the probability that the annual precipitation will be $$b/w$$ $$90$$ cm and $$102$$ cm is

Solution of the differential equation $$3y{{dy} \over {dx}} + 2x = 0$$ represents a family of

The area under the curve shown between $$x=1$$ and $$x=5$$ is to be evaluated using the trapezoidal rule. The following points on the curve are given

The evaluated area (In m²) will be

The value of the integral $$\int\limits_C {{{\cos \left( {2\pi z} \right)} \over {\left( {2z - 1} \right)\left( {z - 3} \right)}}} dz$$ where C is a closed curve given by |z| = 1 is