Final answer:
a. The information provided is inconsistent, and the probability cannot be determined accurately without clarification on the weights of M&M candies.
b. Probability calculation for the mean weight of 465 M&M's requires additional information on the distribution of single M&M weights.
Step-by-step explanation:
There seems to be some inconsistency in the provided information, but I will try to address the issues and provide an approach to calculate the probabilities.
Let's clarify the information:
- It seems like there might be a typo with the values provided for the weights of M&M candies. You mentioned p = .8565 gm and o = .0518 gm, but then you say 7 - .8535 gm, which seems inconsistent.
Assuming you meant to write 7 - .8565 gm and o = .0518 gm, I will proceed with that assumption.
a. Probability that one M&M weighs more than 8.535 grams:
If the weight of one M&M is p = .8565 gm, and you want to find the probability that one M&M weighs more than 8.535 grams, it seems like there might be an issue with the values. Please confirm the correct values for clarity.
b. Probability that 465 M&M's have a mean weight greater than 8.535 grams:
To find the probability that the mean weight of 465 M&M's is greater than 8.535 grams, you need additional information about the distribution of weights or the mean weight of a single M&M. Without this information, it's challenging to calculate the probability accurately.
If you have the mean and standard deviation of the weights of a single M&M, you can use the Central Limit Theorem to approximate the distribution of the sample mean for a large sample size (465) and then find the probability.