Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 72.9 Mbps . The complete list of 50 data speeds has a mean of \( \overline{\mathrm{x}}=17.95 \mathrm{Mbps} \) standard deviation of \( \mathrm{s}=20.42 \mathrm{Mbps} \). a. What is the difference between carrier's highest data speed and the mean of all 50 data speeds? b. How many standard deviations is that [the difference.found in part (a)]? c. Convert the carrier's highest data speed to a z score. d. If we consider data speeds that convert to z scores between -2 and 2 to be neither significantly low nor significantly high, is the carrier's highest data speed significant?

To answer your questions: a. The difference between the carrier's highest data speed (72.9 Mbps) and the mean of all 50 data speeds (17.95 Mbps) is calculated as follows: \[ \text{Difference} = 72.9 - 17.95 = 54.95 \text{ Mbps} \] b. To find how many standard deviations the difference is from the mean, divide the difference by the standard deviation \( s \): \[ \text{Number of standard deviations} = \frac{54.95}{20.42} \approx 2.69 \] c. The z-score is calculated using the formula: \[ z = \frac{(X - \mu)}{s} \] Substituting the values: \[ z = \frac{(72.9 - 17.95)}{20.42} \approx 2.69 \] d. Since the z-score of 2.69 is greater than 2, this indicates that the carrier's highest data speed is significantly high compared to the average data speeds measured at the 50 airports. --- The evolution of mobile data technology has not only transformed how we communicate but has also dramatically changed how we travel. As smartphones leverage high-speed data to enhance travel experiences, we've witnessed the rise of applications that help us navigate airports, book tickets, and even choose optimal flight paths—all in real-time! Moreover, understanding z-scores can be pivotal in making informed decisions! For instance, when analyzing something like user experience data (say, mobile speeds), knowing where values stand relative to the mean can help identify performance outliers—this can inform everything from wireless network upgrades to targeted marketing strategies for tech-savvy travelers!