Final answer:
To find out how many texts you send in a day compared to the average college student, you can calculate a Z-score, which, if negative, indicates fewer texts. Then use the Z-score to determine the percentile and hence the percentage of students who send fewer or more texts. The closest choice to the calculated percentage is 90%. Option C is the correct answer.
Step-by-step explanation:
The question under consideration involves the application of statistical methods to real-life scenarios involving text message usage among college students. Given the average and standard deviation for daily text messages sent or received, we can calculate a Z-score that indicates how a specific value compares to the average in terms of standard deviations.
First, let's calculate how many texts you send in a day and find your z-score:
- Let X be the number of texts you send in a day.
- Assume you send 50 texts per day.
- The Z-score formula is Z = (X - µ) /σ, where µ is the mean and σ is the standard deviation.
- For our example, Z = (50 - 87) / 28 = -1.3214 (approximately).
The Z-score is negative because you send fewer texts than the average student. To find out what percent of college students send fewer or more texts than you, we use the Z-score to look up the corresponding percentile in a standard normal distribution table.
A Z-score of -1.3214 corresponds to a percentile of roughly 9.3%, meaning that about 9.3% of students send fewer texts than you. Consequently, about 90.7% of students send more texts than you.
The closest answer choice among the provided options is therefore c) 90%, which is the correct option.