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 95% of the students? (1 point)
○ 44–80
○ 50–74
○ 38–86
○ 26–98

Explanation:

Step1: Recall Normal Distribution Properties

In a normal distribution, about 68% of data lies within \( \mu \pm \sigma \), 95% within \( \mu \pm 2\sigma \), 99.7% within \( \mu \pm 3\sigma \). Here, \( \mu = 62 \), \( \sigma = 12 \).

Step2: Calculate \( \mu \pm \sigma \)

Lower bound: \( 62 - 12 = 50 \), Upper bound: \( 62 + 12 = 74 \). So 68% of data is between 50 and 74.

Answer:

The interval representing the number of texts sent by 68% of students is 50 - 74 (assuming the last option is 50 - 74, as per normal distribution \( \mu \pm \sigma \) calculation).