The average teenager spends 7.5 hours per week playing computer and video games. In a random sample of 110 teenagers, what is the probability that their mean time for playing games is more than 8 hours per week?

You need some measure of variability to answer the question.

To solve this problem, we need to use the Central Limit Theorem and the concept of the z-score.

The Central Limit Theorem states that the sample mean of a sufficiently large sample follows a normal distribution, regardless of the shape of the population distribution. This theorem allows us to approximate a sample mean using a normal distribution.

The formula for calculating the z-score is:
z = (x - μ) / (σ / √n)
where z is the z-score, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Given information:
- Population mean (μ): 7.5 hours
- Sample size (n): 110 teenagers

We need to find the probability that the mean time for playing games is more than 8 hours per week, which can be transformed into finding the probability that the sample mean is greater than 8 hours.

Step 1: Calculate the sample standard deviation (σ) using the formula for the standard error of the mean:
σ = population standard deviation / √n

Assuming the population standard deviation is unknown, we can use the sample standard deviation as an estimate for it. However, since no information about the sample standard deviation is given in the question, we cannot proceed further without that information.

If you have the sample standard deviation, you can let me know, and I can continue with the calculation for you.