The weight of the eggs produced by a certain breed of hen is normally distributed with mean 66.5 grams (g) and standard deviation 4.6 g. If cartons of such eggs can be considered to be SRSs of size 12 from the population of all eggs, what is the probability that the weight of a carton falls between 775 g and 825 g? (Round your answer to four decimal places.)

Let x be a random variable representing the weight of a carton of egg.

Mean weight of a carton egg = 66.5 x 12 = 798

Combined standard deviation = sqrt (12 (4.6) ^2) = sqrt (253.92) = 15.93

P (775 < x < 825) = P ((775 - 798) / 15.93 < z < (825 - 798) / 15.93) = P (-1.444 < z < 1.695) = P (z < 1.695) - P (z < - 1.444) = P (z < 1.695) - [1 - P (z < 1.444) ] = P (z < 1.695) + P (z < 1.444) - 1 = 0.95496 + 0.92563 - 1 = 0.8806