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?

Table not given, possibly because you cannot copy and paste.

To compute the standard time for the bag-packing task, we will first calculate the average time for filling a bag and then adjust it for the allowance.

a) Computing the standard time for the bag-packing task:
1. Gather the time-study data for the filling activity table given.

| Observation | Time (in seconds) |
|-------------|------------------|
| 1 | 22 |
| 2 | 23 |
| 3 | 25 |
| 4 | 24 |
| 5 | 22 |

2. Calculate the average time for filling a bag by summing the time for each observation and dividing it by the number of observations:
Average Time = (22 + 23 + 25 + 24 + 22) / 5 = 116 / 5 = 23.2 seconds

3. Apply the allowance for workers, which is 23% of the average time:
Allowance = 0.23 * 23.2 = 5.336 seconds

4. Calculate the standard time by adding the average time and the allowance:
Standard Time = Average Time + Allowance = 23.2 + 5.336 = 28.536 seconds
Therefore, the standard time for the bag-packing task is 28.536 seconds.

b) To determine the number of observations necessary for 99% confidence within 5% accuracy, we can use the formula for sample size determination:

n = (Z^2 * s^2) / (E^2)

Where:
n = sample size
Z = Z-score at the desired confidence level (for 99% confidence, Z = 2.58)
s = standard deviation of the observations (unknown in this case)
E = desired accuracy (5% or 0.05 in decimal form)

1. Estimate the standard deviation of the observations from the sample data:
To estimate the standard deviation, we can use the formula for the sample standard deviation (s) of a population as an approximation:
s = (√((∑(x - x̅)^2) / (n - 1))

Where:
x = individual observation
x̅ = mean of the observations
n = total number of observations

Using the time-study data table, the mean (x̅) is 23.2 seconds and the number of observations (n) is 5.
Calculate the sum of the squared differences from the mean (∑(x - x̅)^2):
((22 - 23.2)^2) + ((23 - 23.2)^2) + ((25 - 23.2)^2) + ((24 - 23.2)^2) + ((22 - 23.2)^2) = 7.2

Calculate the estimated standard deviation (s):
s = (√(7.2 / (5 - 1))) ≈ 1.732

2. Substitute the values into the formula for sample size determination:
n = (2.58^2 * 1.732^2) / (0.05^2)
n ≈ 134.4384

Since the sample size must be a whole number, we round up to the nearest integer:
n ≈ 135

Therefore, to achieve 99% confidence within 5% accuracy, you would need approximately 135 observations.