Answer:
The chance of completing the entire package installation in under 12 minutes is 0.1271.
Step-by-step explanation:
We define X as a normal distribution representing the time taken in seconds to install the software. According to the Central Limit Theorem, X is approximately normal, where the mean is 15 and variance is 15, giving a standard deviation of √15 = 3.873.
To find the probability of the total installation lasting less than 12 minutes, which equals 720 seconds, each installation should average under 720/68 = 10.5882 seconds. Thus, we seek the probability that X is less than 10.5882. To do this, we will apply W, the standard deviation value of X, calculated via the formula provided.
Utilizing , we reference the cumulative distribution function of the standard normal variable W, with values found in the attached file.
Given the symmetry of the standard normal distribution density function, we ascertain .
Consequently, the probability that the installation process for the entire package is completed within 12 minutes is 0.1271.