Question 1198232
**1. Define the Problem**

* We want to find the probability of spending more than 1 minute (60 seconds) to download the file.
* Mean download time (μ) = 40 seconds
* Standard deviation (σ) = 5 seconds

**2. Calculate the Number of Standard Deviations**

* Difference from the mean: 60 seconds - 40 seconds = 20 seconds
* Number of standard deviations (k): 20 seconds / 5 seconds = 4

**3. Apply Chebyshev's Inequality**

* Chebyshev's Inequality states that for any dataset, the proportion of data that lies within 'k' standard deviations of the mean is at least 1 - (1/k²).

* In this case, k = 4.

* Probability of data within 4 standard deviations of the mean: 
    * 1 - (1/4²) = 1 - (1/16) = 15/16 = 0.9375

* This means at least 93.75% of the download times will fall within 4 standard deviations of the mean (between 0 and 80 seconds).

**4. Determine the Probability of Spending More Than 1 Minute**

* Since we want the probability of spending *more* than 1 minute (60 seconds), we are looking at the probability of values outside of 4 standard deviations from the mean.

* Probability of spending more than 1 minute: 
    * 1 - Probability of spending within 4 standard deviations 
    * 1 - 0.9375 = 0.0625

**Therefore, according to Chebyshev's Inequality, the probability of spending more than 1 minute to download the file is at most 0.0625 or 6.25%.**

**Important Note:**

* Chebyshev's Inequality provides an upper bound on the probability. The actual probability could be lower. 
* If the distribution of download times were known (e.g., normal distribution), we could use more precise methods (like the z-score table) to calculate the exact probability.