Question
A survey of high school girls found that the mean number of text messages sent per day by the girls was 62, with a standard deviation of 12. If a normal distribution is assumed, which interval represents the number of texts sent by 68.2% of the girls?
38−86
44-80
50-74
56-68
38−86
44-80
50-74
56-68
Answers
GPT-4o mini
To find the interval that represents the number of texts sent by 68.2% of high school girls, we can use the properties of the normal distribution. According to the empirical rule (also known as the 68-95-99.7 rule):
- Approximately 68% of the data falls within one standard deviation of the mean.
Given that the mean number of text messages sent is 62, and the standard deviation is 12, we can calculate the interval for 68.2% of the girls as follows:
1. Mean: \( \mu = 62 \)
2. Standard deviation: \( \sigma = 12 \)
Now, we will calculate one standard deviation below and one standard deviation above the mean:
- 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 68.2% of the girls is \( 50-74 \).
Therefore, the correct answer is **50-74**.
- Approximately 68% of the data falls within one standard deviation of the mean.
Given that the mean number of text messages sent is 62, and the standard deviation is 12, we can calculate the interval for 68.2% of the girls as follows:
1. Mean: \( \mu = 62 \)
2. Standard deviation: \( \sigma = 12 \)
Now, we will calculate one standard deviation below and one standard deviation above the mean:
- 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 68.2% of the girls is \( 50-74 \).
Therefore, the correct answer is **50-74**.