Total sample size from histogram

5 Each father in a random sample of fathers was asked how old he was when his first child was born. The following histogram represents the information.
\includegraphics[max width=\textwidth, alt={}, center]{14e8a601-2180-4491-9336-cafd262f2596-3_789_1627_1468_260}

1. What is the modal age group?
2. How many fathers were between 25 and 30 years old when their first child was born?
3. How many fathers were in the sample?
4. Find the probability that a father, chosen at random from the group, was between 25 and 30 years old when his first child was born, given that he was older than 25 years. 632 teams enter for a knockout competition, in which each match results in one team winning and the other team losing. After each match the winning team goes on to the next round, and the losing team takes no further part in the competition. Thus 16 teams play in the second round, 8 teams play in the third round, and so on, until 2 teams play in the final round.

7 Kareem bought some tomatoes. He recorded the mass of each tomato and displayed the results in a histogram, which is shown below.
\includegraphics[max width=\textwidth, alt={}, center]{57007d39-abb0-475e-9ed8-03021fa1273b-05_1273_1849_363_109} Determine how many tomatoes Kareem bought.
[0pt] [2] Answer all the questions.
Section B (77 marks)

2. The time taken to complete a puzzle, in minutes, is recorded for each person in a club. The times are summarised in a grouped frequency distribution and represented by a histogram. One of the class intervals has a frequency of 20 and is shown by a bar of width 1.5 cm and height 12 cm on the histogram. The total area under the histogram is \(94.5 \mathrm {~cm} ^ { 2 }\) Find the number of people in the club.
(3)
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1. The time taken to complete a puzzle, in minutes, is recorded for each person in a club. The times are summarised in a grouped frequency distribution and represented by a histogram.

One of the class intervals has a frequency of 20 and is shown by a bar of width 1.5 cm and height 12 cm on the histogram. The total area under the histogram is \(94.5 \mathrm {~cm} ^ { 2 }\) Find the number of people in the club.

1. A teacher recorded, to the nearest hour, the time spent watching television during a particular week by each child in a random sample. The times were summarised in a grouped frequency table and represented by a histogram.

One of the classes in the grouped frequency distribution was 20-29 and its associated frequency was 9. On the histogram the height of the rectangle representing that class was 3.6 cm and the width was 2 cm .

1. Give a reason to support the use of a histogram to represent these data.
2. Write down the underlying feature associated with each of the bars in a histogram.
3. Show that on this histogram each child was represented by \(0.8 \mathrm {~cm} ^ { 2 }\). The total area under the histogram was \(24 \mathrm {~cm} ^ { 2 }\).
4. Find the total number of children in the group.

1. The histogram shows information about the lengths, \(l\) centimetres, of a sample of worms of a certain species.
\includegraphics[max width=\textwidth, alt={}, center]{c5ea8584-939f-4627-8f81-bac60233d9a3-04_913_1303_392_175} The number of worms in the sample with lengths in the class \(3 \leqslant l < 4\) is 30 .

1. Find the number of worms in the sample with lengths in the class \(0 \leqslant l < 2\).
2. Find an estimate of the number of worms in the sample with lengths in the range \(4.5 \leqslant l < 5.5\).
   [0pt] [BLANK PAGE]

9 The histogram shows information about the numbers of cars in five different price ranges, sold in one year at a car showroom.
\includegraphics[max width=\textwidth, alt={}, center]{4ba60d6b-c987-4f6b-8c55-8b594c90c854-06_922_1413_495_244} It is given that 66 cars in the price range \(\pounds 10000\) to \(\pounds 20000\) were sold.

1. Find the number of cars sold in the price range \(\pounds 50000\) to \(\pounds 90000\).
2. State the units of the frequency density.
3. Suggest one change that the management could make to the diagram so that it would provide more information.
4. Estimate the number of cars sold in the price range \(\pounds 50000\) to \(\pounds 60000\).