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6.2 The Normal Distribution (pp. 220-231) You are not required to memorize the formula for the normal probability density function, but rather know the properties (symmetry and bell shape).
The Normal Probability Function: Tables of Certain Area-Ordinate Ratios and of Their Reciprocals, Biometrika, Vol. 42, No. 1/2 (Jun., 1955), pp. 217-222 ...
Leo A. Aroian, The Probability Function of the Product of Two Normally Distributed Variables, The Annals of Mathematical Statistics, Vol. 18, No. 2 (Jun., 1947), pp. 265-271 ...