What should be the transmission bandwidth if an FM signal with 75kHz deviation and highest frequency of modulation 15kHz?

Hint:The bandwidth of a frequency modulated, FM signal depends on a spread of things including the extent and frequency of the modulation, and their levels are important for broadcast and radio communication applications. During this problem we'd like to seek out the transmission bandwidth that's needed for given deviation frequency and modulation frequency. To find out the bandwidth we use the formula $BW = 2(\Delta f + {f_m})$ where Δ f = deviation frequency and fm is the modulation frequency.

Complete step by step solution:
A very useful rule of thumb employed by many engineers to work out the bandwidth of an FM signal for broadcast and radio communication systems is understood as Carson’s Rule. This rule states that 98% of the signal power is contained within bandwidth adequate to deviation frequency, plus the modulation frequency doubled. Carson’s rule is often expressed simply as formula
$\begin{gathered}
  BW = 2(\Delta f + {f_m}) \\
   \Rightarrow BW = 2(75 + 15) \\
   \Rightarrow BW = 180KHz \\
    \\
\end{gathered} $
Now we consider the information that we've within the question as
Δ f = deviation frequency = 75kHz
fm= modulation frequency =15kHz
BW= Bandwidth for 98% power.
Now substituting the corresponding values in above formula, we get
$
  BW = 2(\Delta f + {f_m}) \\
   \Rightarrow BW = 2(75 + 15) \\
   \Rightarrow BW = 180KHz \\
    \\
 $

Note:
Frequency modulation (FM) is the encoding of data during a carrier by varying the instantaneous frequency of the wave. The term and technology are utilized in computing, signal processing and telecommunications. To provide conveniently spaced channels 200 kHz is allowed for every station. This rule is additionally very useful when determining the bandwidth of the many two-way radio communications systems. These use narrow band FM, and it's particularly important that the sidebands don't cause interference to adjacent channels which will be occupied by other users.