1 O/N 19/P21/Q2

(a) One afternoon, there were 200 visitors to a library.

[tex]\[

\begin{tabular}{|c|c|c|c|c|c|}

\hline

Class Interval & $0\ \textless \ t \leqslant 20$ & $20\ \textless \ t \leqslant 40$ & $40\ \textless \ t \leqslant 60$ & $60\ \textless \ t \leqslant 90$ & $\leqslant 180$ \\

\hline

Class Width & 20 & 20 & 20 & 30 & \\

\hline

Frequency & 26 & 76 & 56 & 24 & 18 \\

\hline

Frequency Density & 1.3 & 3.8 & 2.8 & 0.8 & 0.2 \\

\hline

\end{tabular}

\][/tex]

(i) On the grid, draw a histogram to represent this data.

(ii) Work out the percentage of these visitors who spent more than 40 minutes in the library.

Sure! Let's work through the problem step by step.

### Step 1: Understand the Data
We have a table of data about visitors to a library. The data are divided into different intervals of time spent in the library, but we are particularly interested in visitors who spent more than 40 minutes there.

### Step 2: Determine Frequency for Relevant Intervals
To find the total number of visitors who spent more than 40 minutes in the library, we need to look at the given frequencies for time intervals:

- Interval 40: Frequency = 56
- Interval 60: Frequency = 24

These intervals represent the visitors who spent more than 40 minutes in the library.

### Step 3: Add Frequencies
Add together the frequencies for the intervals of interest:

- Total visitors who spent more than 40 minutes = 56 (from 40
### Step 4: Calculate the Percentage
Now, calculate the percentage of the total number of visitors (200) who spent more than 40 minutes in the library:

[tex]\[ \text{Percentage} = \left(\frac{\text{Visitors more than 40 minutes}}{\text{Total visitors}}\right) \times 100 \][/tex]
[tex]\[ \text{Percentage} = \left(\frac{80}{200}\right) \times 100 = 40\% \][/tex]

### Conclusion
So, 80 visitors spent more than 40 minutes in the library, which is 40% of the total visitors.