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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!

Suppose that the mean time someone spends using a device with a screen such as a smartphone, computer, or television is 8.35 hours. Use a normal probability distribution with a standard deviation of 1.9 hours to answer the following questions about daily screen time:

a. What is the probability that a randomly selected person has between 3 and 8 hours of screen time a day?

b. How many hours of screen time must a person have in order to be in the top 3% of all screen time values?

c. What is the probability that a person has more than 5 hours of screen time a day?

This problem explores daily screen time through a normal distribution with a mean of 8.35 hours and a standard deviation of 1.9 hours. Learn how to calculate the probability of screen time within specific ranges, as well as the screen time value for the top 3% of users.

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