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
56–68
56–68
38–86
38–86
44–80
44–80
50–74
Responses
56–68
56–68
38–86
38–86
44–80
44–80
50–74
Answers
GPT-4o mini
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.
Given:
- Mean (μ) = 62
- Standard Deviation (σ) = 12
To find the interval representing 68% of the students, we calculate one standard deviation below and above the mean:
Lower limit: μ - σ = 62 - 12 = 50
Upper limit: μ + σ = 62 + 12 = 74
Thus, the interval representing the number of texts sent by 68% of the students is **50–74**.
Given:
- Mean (μ) = 62
- Standard Deviation (σ) = 12
To find the interval representing 68% of the students, we calculate one standard deviation below and above the mean:
Lower limit: μ - σ = 62 - 12 = 50
Upper limit: μ + σ = 62 + 12 = 74
Thus, the interval representing the number of texts sent by 68% of the students is **50–74**.