Question

Assume the weight of bags of M&Ms can be modeled with the normal distribution with mean 50 grams and standard deviation 1 gram. According to the Empirical Rule or 68-95-99.7 rule, 68% of all M&M bags will have weights between _______ and 51 grams.

Answer 1

Since the weight of bags of M&Ms can be modeled with a normal distribution with mean 50 grams and standard deviation 1 gram, we can use the Empirical Rule to estimate the percentage of bags that weigh between two values. According to the Empirical Rule, 68% of all observations fall within one standard deviation of the mean. So, in this case, we can say that 68% of all M&M bags will have weights between:

Mean - 1 standard deviation = 50 - 1(1) = 49 grams
and
Mean + 1 standard deviation = 50 + 1(1) = 51 grams

Therefore, 68% of all M&M bags will have weights between 49 and 51 grams.