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A doctor's office has five doctors. This morning, 24 patients visited the office. Each patient saw one of the five doctors.

(a) The doctor each patient went to see appears below.
([tex]$F =$[/tex] Dr. Foster, [tex]$M =$[/tex] Dr. Mitchell, [tex]$P =$[/tex] Dr. Phillips, [tex]$T =$[/tex] Dr. Tran, [tex]$W =$[/tex] Dr. Washington)

Complete the frequency distribution for the data.
[tex]\[
\begin{tabular}{|llllllll|}
\hline
\multicolumn{10}{|c|}{ Doctor } \\
\hline
W & F & M & W & P & F & M & F \\
P & W & F & M & F & W & P & T \\
T & P & T & M & W & M & F & W \\
\hline
\end{tabular}
\][/tex]
[tex]\[
\begin{tabular}{cc}
Doctor & Frequency \\
\hline
F & $\square$ \\
M & $\square$ \\
P & $\square$ \\
T & $\square$ \\
W & $\square$
\end{tabular}
\][/tex]

(b) These doctors are affiliated with four major medical groups. Not every doctor is affiliated with every group. The table below shows the groups and the doctors affiliated with them.
[tex]\[
\begin{tabular}{|c|c|}
\hline
Medical group & Doctor \\
\hline
City Med & F and T \\
\hline
Bayside & M and T \\
\hline
Plymouth & W \\
\hline
Coast & F, P, and W \\
\hline
\end{tabular}
\][/tex]

How many patients went to see a doctor affiliated with the City Med medical group?
[tex]$\square$[/tex] patients

Sagot :

GinnyAnsweridn
Sure, I will guide you step-by-step to solve the problem.

### (a) Completing the frequency distribution

#### Given Data
The doctors the patients went to see:
[tex]\[ W, F, M, W, P, F, M, F, P, W, F, M, F, W, P, T, T, P, T, M, W, M, F, W \][/tex]

#### Frequency Distribution Table
To find the frequencies, count how many times each doctor appears in the data set:

- Dr. Foster (F): Count the occurrences of 'F'.
- F appears 6 times.
- Dr. Mitchell (M): Count the occurrences of 'M'.
- M appears 5 times.
- Dr. Phillips (P): Count the occurrences of 'P'.
- P appears 4 times.
- Dr. Tran (T): Count the occurrences of 'T'.
- T appears 3 times.
- Dr. Washington (W): Count the occurrences of 'W'.
- W appears 6 times.

After counting, we get the following frequency distribution:

[tex]\[ \begin{tabular}{cc} Doctor & Frequency \\ \hline F & 6 \\ M & 5 \\ P & 4 \\ T & 3 \\ W & 6 \\ \end{tabular} \][/tex]

### (b) Patients who saw a doctor affiliated with City Med

#### City Med Affiliation
According to the given medical group affiliations:
- City Med: Dr. Foster (F) and Dr. Tran (T).

To find out how many patients saw a City Med-affiliated doctor, sum the frequencies of Dr. Foster (F) and Dr. Tran (T):

- Frequency of Dr. Foster (F) is 6.
- Frequency of Dr. Tran (T) is 3.

Adding these frequencies together:
[tex]\[ 6 + 3 = 9 \][/tex]

Thus, the number of patients who went to see a doctor affiliated with the City Med medical group is:
[tex]\[ 9 \text{ patients} \][/tex]

So, summarizing the solution:

### (a) Frequency Distribution
[tex]\[ \begin{tabular}{cc} Doctor & Frequency \\ \hline F & 6 \\ M & 5 \\ P & 4 \\ T & 3 \\ W & 6 \\ \end{tabular} \][/tex]

### (b) Number of Patients for City Med
[tex]\[ 9 \text{ patients} \][/tex]
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