Question

because of the wavelengths used in different kinds of radio broadcasting, am radio signals often travel farther than fm radio signals do. here are some summary statistics for the broadcasting ranges of radio stations in one region.
type of station mean broadcast range standard deviation
am $mu = 320$ km $sigma = 80$ km
fm $mu = 88$ km $sigma = 5$ km
the khan radio station is an am station with a broadcast range of 352 km, and the kfal radio station is an fm station with a broadcast range of 90 km.
relative to its station type, which station broadcasts farther?
choose 1 answer:

Explanation:

Step1: Calculate z-score for AM station

The z-score formula is $z = \frac{x - \mu}{\sigma}$. For KHAN (AM):
$z = \frac{352 - 320}{80}$

Step2: Compute AM z-score value

$\frac{32}{80} = 0.4$

Step3: Calculate z-score for FM station

For KFAL (FM):
$z = \frac{90 - 88}{5}$

Step4: Compute FM z-score value

$\frac{2}{5} = 0.4$

Step5: Compare z-scores

Both stations have the same z-score, meaning they are equally far relative to their station type.

Answer:

Relative to their station types, KHAN (AM) and KFAL (FM) broadcast equally far (both have a z-score of 0.4).