Question

A Folgers Black Silk K-Cup coffee pod weigh on average .28 oz with a standard deviation of .05 Oz answer to the questions.

1.) what percentage of K-cups can be expected to fall within two standard deviations of the mean?
2.) what is the probability that a K-Cup will have more than three .33 oz?
3.) K-Cups that are more than two standard deviations below the mean are considered to be weak. What percentage of K-Cup are considered to be weak?
4 ) in a standard box of 44 K Cups, how many will weigh between .23 and .38 Oz?
5.Sam's Club sells K-Cups in a box of 128. How many of them will weigh less than 23 Oz?
6.) the ideal weight for K-Cups are within one standard deviation of the mean, how many of the Sam's Clubs box of K-cups are ideal? ​

Answer 1

1. Approximately 95% of K-Cups can be expected to fall within two standard deviations of the mean.

2. The probability that a K-Cup will have more than 0.33 oz is about 30.85%.

3. About 2.5% of K-Cups are considered weak, falling more than two standard deviations below the mean.

Explanation:

The normal distribution of weights for Folgers Black Silk K-Cup coffee pods with a mean of 0.28 oz and a standard deviation of 0.05 oz provides valuable insights into the distribution of weights. In the context of standard deviations, approximately 95% of K-Cups can be expected to fall within two standard deviations of the mean. This is a fundamental concept in statistics, illustrating the typical range of weights and indicating that the majority of K-Cups conform to this expected variation.

Moving to the probability of a K-Cup weighing more than 0.33 oz, this is calculated using the normal distribution probabilities. The result, approximately 30.85%, offers a quantitative understanding of the likelihood of encountering K-Cups with weights exceeding the specified threshold. For K-Cups considered weak—falling more than two standard deviations below the mean—the percentage is about 2.5%. This signifies a relatively low occurrence of weaker K-Cups, highlighting the robustness of the manufacturing process within the specified weight range.

In summary, these statistical measures not only provide a comprehensive overview of the distribution of weights for Folgers Black Silk K-Cups but also offer valuable insights into the probabilities associated with different weight ranges, aiding in quality control and consumer expectations.