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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 56–68 56–68 44–80 44–80 38–86 38–86 50–74

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To find the interval that represents the number of text messages sent by 68% of students, we can use the empirical rule (also known as the 68-95-99.7 rule) associated with a normal distribution.

According to the empirical rule:

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

Here, the mean number of text messages sent is 62, and the standard deviation is 12.

To find the interval that includes 68% of the students:

  1. Calculate one standard deviation below and above the mean.
    • Mean - 1 standard deviation: \( 62 - 12 = 50 \)
    • Mean + 1 standard deviation: \( 62 + 12 = 74 \)

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