A zoo is concerned that some of their jaguars may be becoming slightly overweight. Suppose that the weight (in kg) of a jaguar in this zoo is normally distributed with mean 59 and variance 256. Assume that jaguar weights are independent. Any jaguar that weighs more than 77 kgs is considered slightly overweight and will need to go on a special "healthy" diet.

In a random sample of 12 jaguars at this zoo, find the probability that more than 2 will need to go on the special healthy diet. The answer is rounded to four decimal places