Question

An airline is considering charging a​ two-tiered rate for checked bags based on their weight. Before deciding at what weight to increase the​ rate, the airline wishes to estimate the mean weight per bag checked by passengers. It wants the estimate to be within plus or minus±0.50 pounds of the true population mean. A pilot sample of checked bags produced the results shown below. 37 41 42 38 48 32 42 32 32 43 47 33 31 42 45 41 34 41 49 32

a. What sample size should the airline use if it wants to have 95​% ​confidence? __________ (round up to the nearest whole number)

b. What could the managers do to lower the required sample​size? Select all that apply.

A. Reduce the level of confidence

B. Increase the population standard deviation

C. Increase the margin of error

D. Use a larger pilot sample

Answer 1

The percent uncertainty of the bag's weight is 8%. This is calculated by dividing the uncertainty by the expected value (0.4/5) and multiplying by 100%. If the expected weight of the bag decreased to 2.5 lb with the same uncertainty, the percent uncertainty would be 16%.

Step-by-step explanation:

To determine the percent uncertainty of a 5-pound bag's weight that has an uncertainty of ±0.4 pounds, we first observe that the expected value of the bag's weight, A, is 5 pounds. The uncertainty in this value, ∆A, is 0.4 pounds. We use the following equation to determine the percent uncertainty of the weight:

Percent Uncertainty = (Uncertainty / Expected value) × 100%

Substituting the given values, we get:

Percent Uncertainty = (0.4 / 5) × 100% = 0.08 × 100% = 8%

This indicates that the weight of the 5 lb bag has a percent uncertainty of 8%. If we consider the same uncertainty for a bag that is half as heavy, the percent uncertainty would double because:

Percent Uncertainty for 2.5 lb bag = (0.4 / 2.5) × 100% = 0.16 × 100% = 16%

This calculation shows that as the expected weight of an item decreases while the uncertainty remains the same, the percent uncertainty increases.