The Dubuque Cement Company packs 80-pound bags of concrete mix. Time-study data for the filling activity are shown in the following table. Because of the high physical demands of the job, the company's policy is a 23% allowance for workers. a) Compute the standard time for the bag-packing task. b) How many observations are necessary for 99% confidence, within 5% accuracy?

To compute the standard time for the bag-packing task, we need to follow these steps:

Step 1: Calculate the observed time (OT) for each observation by adding the actual time taken for each bag packing task.
Step 2: Calculate the average observed time (AOT) by summing up all the observed times and dividing by the number of observations.
Step 3: Compute the standard time (ST) using the formula:

ST = AOT x (1 + Allowance%)

In this case, the allowance is 23%, so we can substitute it into the formula:

ST = AOT x (1 + 0.23)

Now, let's move to part b) and determine the number of observations needed for 99% confidence within 5% accuracy.

To calculate the required sample size, we need to use a statistical formula called the sample size formula:

n = (Z^2 * σ^2) / E^2

where:
n = required sample size
Z = Z-value corresponding to the desired level of confidence (in this case, 99% confidence)
σ = standard deviation of the population (unknown in this case)
E = desired level of accuracy (in this case, 5%)

To find the value of Z for 99% confidence, we can refer to a standard normal distribution table or use statistical software. The Z-value for 99% confidence is approximately 2.58.

Since the standard deviation (σ) is unknown in this case, we can use a conservative estimate. A common estimate is to assume a standard deviation equal to the range of values observed (highest - lowest).

Now, with all the necessary information, we can calculate the required sample size (n) using the sample size formula.