The image contains a problem involving a normal distribution for daily screen time. Here's a breakdown of the key details:

• Mean screen time ($\mu$) = 8.35 hours
• Standard deviation ($\sigma$) = 1.9 hours
• The questions involve finding probabilities and specific values related to the normal distribution.

Solutions:

a. Probability between 3 and 8 hours of screen time

• The probability is given as 0.5395. This likely involves calculating the area under the normal curve between 3 and 8 hours using a Z-table or a calculator.

b. Hours of screen time to be in the top 3%

• The required screen time is 16.18 hours. This corresponds to the 97th percentile of the distribution (top 3%).

c. Probability of more than 5 hours of screen time

• The probability is 0.9099. This involves finding the area under the normal curve to the right of 5 hours.

Would you like a detailed explanation of any of these calculations or a step-by-step breakdown?

Here are 5 follow-up questions that could expand on this topic:

1. How do you calculate the Z-score for a specific value in a normal distribution?
2. What is the relationship between percentiles and Z-scores?
3. How can the area under the normal curve be used to find probabilities?
4. Why is it important to understand the concept of standard deviation in real-world contexts?
5. How would the answers change if the standard deviation were larger or smaller?

Tip: When working with normal distributions, always remember to convert raw scores to Z-scores for easier probability lookup!