To find the probability that the mean level of social media use in the sample will be 4 hours per week or more, we need to calculate the Z-score for 4 hours and then find the corresponding probability from the standard normal distribution.

Step 1: Calculate the Z-score

The formula for the Z-score is:

$Z = \frac{X - \mu}{\sigma / \sqrt{n}}$

Where:

• $X$ is the sample mean (4 hours)
• $\mu$ is the population mean (3.2 hours)
• $\sigma$ is the population standard deviation (1.6 hours)
• $n$ is the sample size

Since a large random sample is being taken, we can use the Central Limit Theorem, which states that the sampling distribution of the sample mean is approximately normal for large $n$. We can proceed without knowing the exact sample size because the standard error will still be valid as long as $n$ is large.

Step 2: Plug in the values

Let's rewrite the Z-score formula:

$Z = \frac{4 - 3.2}{1.6 / \sqrt{n}}$

Since the sample size $n$ is large, we can assume that the standard error of the mean ($\sigma / \sqrt{n}$) approaches zero. Therefore, we can look up the Z value using the standard normal distribution tables or software for exact probabilities.