Final answer:
To estimate the average time required for a beginner to become proficient with a new software function to within 6 minutes at a 99% confidence level, a sample size of 174 is required, given a known standard deviation of 24 minutes.
Step-by-step explanation:
The problem involves determining the sample size necessary for a computer software company to estimate the average time it takes for a beginner to become proficient at creating a graph using their spreadsheet package with a given level of confidence and margin of error.
The known standard deviation (σ) of the past experiences is 24 minutes, and the desired margin of error (E) is 6 minutes.
To obtain this estimate within a 99% confidence interval, we use the z-score associated with a 99% confidence level, which is approximately 2.576.
The formula for finding the sample size (n) when the population standard deviation is known is:
n = (z * σ / E)^2
Plugging in the values we get:
n = (2.576 * 24 / 6)^2
n ≈ 173.29
Since we cannot have a fraction of a sample, we round up to the nearest whole number. Therefore, the required sample size is 174.