Question

A survey of high school students found that the mean number of text messages sent per day was 62, with a standard deviation of 12. If a normal distribution is assumed, which interval represents the number of texts sent by 68% of the students?(1 point)
Responses

50–74
50–74

44–80
44–80

56–68
56–68

38–86

Answer 1

To determine the interval representing the number of text messages sent by 68% of the students, we can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normal distribution:

- Approximately 68% of the data falls within one standard deviation of the mean.

Given the mean (\( \mu \)) is 62 and the standard deviation (\( \sigma \)) is 12, we can calculate the interval for 68% of the students:

1. Mean: \( \mu = 62 \)
2. One standard deviation: \( \sigma = 12 \)

The interval is calculated as:
- Lower bound: \( \mu - \sigma = 62 - 12 = 50 \)
- Upper bound: \( \mu + \sigma = 62 + 12 = 74 \)

Thus, the interval that represents the number of texts sent by 68% of the students is **50–74**.