Question

Let x represent the weight of a randomly selected bag. For what value of c is P(e(x) - c < x < e(x) + c) = 0.82? Give your answer to four decimal places.

Answer 1

Without complete information, the precise value of c cannot be calculated. However, the percent uncertainty of a 5 lb bag with an uncertainty of ±0.4 lb can be found to be 8% using the formula (SA / A) × 100%.

Step-by-step explanation:

The question revolves around finding a particular value of c for a normal distribution, where the probability of the weight of a randomly selected bag being within the range of expected value minus c to expected value plus c equals 0.82. To find this value, we would typically use the properties of the normal distribution, most likely looking up values in a standard normal distribution table or using a calculator with statistical functions. However, as the question is incomplete and does not provide enough information, we cannot calculate the precise value of c. For instance, details about the expected value e(x) or whether c refers to a multiple of the standard deviation are missing, which are crucial pieces of information needed for this problem.

However, we can calculate the percent uncertainty for the other problem mentioned. When we know the expected value of a bag's weight (A) is 5 lb, and the uncertainty in this value (SA) is 0.4 lb, we use the formula:

Percent Uncertainty = (SA / A) × 100%

This would result in:

Percent Uncertainty = (0.4 lb / 5 lb) × 100% = 8% uncertainty.