IB Questionbank Test



2.5 1a. [1 mark] The histogram shows the lengths of 25 metal rods, each measured correct to the nearest cm.Write down the modal length of the rods. 1b. [3 marks] Find the median length of the rods. 1c. [1 mark] The upper quartile is 4?cm.Calculate?the lower quartile. 1d. [1 mark] Calculate the interquartile range. 2a. [2 marks] The final examination results obtained by a group of 3200 Biology students are summarized on the cumulative frequency graph.Find?the median of the examination results. 2b. [3 marks] Find the interquartile range. 2c. [2 marks] 350 of the group obtained the highest possible grade in the examination.Find the final examination result required to obtain the highest possible grade. 2d. [2 marks] The grouped frequency table summarizes the examination results of this group of students.Write down?the modal class. 2e. [1 mark] Write down the mid-interval value of the modal class. 2f. [2 marks] Calculate an estimate of?the mean examination result. 2g. [1 mark] Calculate an estimate of the standard deviation, giving your answer correct to three decimal places. 2h. [3 marks] The teacher sets a grade boundary that is one standard deviation below the mean.Use the cumulative frequency graph to estimate the number of students whose final examination result was below this grade boundary. 3a. [2 marks] Each month the number of days of rain in Cardiff is recorded.The following data was collected over a period of 10 months.11 13 8 11 8 7 8 14 x 15For these data the median number of days of rain per month is 10.Find the value of x. 3b. [2 marks] Find?the standard deviation 3c. [2 marks] Find?the interquartile range. 4a. [1 mark] In a high school, 160 students completed a questionnaire which asked for the number of people they are following on a social media website. The results were recorded in the following box-and-whisker diagram.Write down the median. 4b. [2 marks] The following incomplete table shows the distribution of the responses from these 160 plete the table. 4c. [1 mark] Write down the mid-interval value for the 100 < x ≤ 150 group. 4d. [2 marks] Using the table, calculate an estimate for the mean number of people being?followed on the social media website by these 160 students. 5a. [1 mark] The histogram shows the time, t, in minutes, that it takes the customers of a restaurant to eat their lunch on one particular day. Each customer took less than 25 minutes.The histogram is incomplete, and only shows data for 0 ≤ t < 20.Write down the mid-interval value for 10 ≤ t < 15. 5b. [1 mark] The mean time it took all customers to eat their lunch was estimated to be 12 minutes.It was found that k customers took between 20 and 25 minutes to eat their lunch.Write down the total number of customers in terms of k. 5c. [3 marks] Calculate the value of k. 5d. [1 mark] Hence, complete the histogram. 6a. [1 mark] On one day 180 flights arrived at a particular airport. The distance travelled and the arrival status for each incoming flight was recorded. The flight was then classified as on time, slightly delayed, or heavily delayed.The results are shown in the following table.A χ2 test is carried out at the 10 % significance level to determine whether the arrival status of incoming flights is independent of the distance travelled.State the alternative hypothesis. 6b. [2 marks] Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed. 6c. [1 mark] Write down the number of degrees of freedom. 6d. [2 marks] Write down?the χ2 statistic. 6e. [1 mark] Write down?the associated p-value. 6f. [2 marks] The critical value for this test is 7.779.State, with a reason, whether you would reject the null hypothesis. 6g. [2 marks] A flight is chosen at random from the 180 recorded flights.Write down the probability that this flight arrived on time. 6h. [2 marks] Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km. 6i. [3 marks] Two flights are chosen at random from those which were slightly delayed.Find the probability that each of these flights travelled at least 5000 km. 7a. [2 marks] A transportation company owns 30 buses. The distance that each bus has travelled since being purchased by the company is recorded. The cumulative frequency curve for these data is shown.Find the number of buses that travelled a distance between 15000 and 20000 kilometres. 7b. [2 marks] Use the cumulative frequency curve to find the?median distance. 7c. [1 mark] Use the cumulative frequency curve to find the?lower quartile. 7d. [1 mark] Use the cumulative frequency curve to find the upper quartile. 7e. [1 mark] Hence write down the interquartile range. 7f. [1 mark] Write down the percentage of buses that travelled a distance greater than the upper quartile. 7g. [1 mark] Find the number of buses that travelled a distance less than or equal to 12?000 km. 7h. [2 marks] It is known that 8 buses travelled more than m kilometres.Find the value of m. 7i. [4 marks] The smallest distance travelled by one of the buses was 2500 km.The longest distance travelled by one of the buses was 23 000 km.On graph paper, draw a box-and-whisker diagram for these data. Use a scale of 2 cm to represent 5000 km. 8a. [2 marks] A group of 20 students travelled to a gymnastics tournament together. Their ages, in years, are given in the following table.For the students in this group find the mean age; 8b. [1 mark] For the students in this group write down the median age. 8c. [3 marks] The lower quartile of the ages is 16 and the upper quartile is 18.5.Draw a box-and-whisker diagram, for these students’ ages, on the following grid. 9a. [1 mark] A group of 800 students answered 40 questions on a category of their choice out of History, Science and Literature.For each student the category and the number of correct answers, , was recorded. The results obtained are represented in the following table.State whether is a discrete or a continuous variable. 9b. [1 mark] Write down, for , the modal class; 9c. [1 mark] Write down, for , the mid-interval value of the modal class. 9d. [2 marks] Use your graphic display calculator to estimate the mean of ; 9e. [1 mark] Use your graphic display calculator to estimate the standard deviation of . 9f. [2 marks] A test at the 5% significance level is carried out on the results. The critical value for this test is 12.592.Find the expected frequency of students choosing the Science category and obtaining 31 to 40 correct answers. 9g. [1 mark] Write down the null hypothesis for this test; 9h. [1 mark] Write down the number of degrees of freedom. 9i. [1 mark] Write down the -value for the test; 9j. [2 marks] Write down the statistic. 9k. [2 marks] State the result of the test. Give a reason for your answer. 10a. [1 mark] A tetrahedral (four-sided) die has written on it the numbers 1, 2, 3 and 4. The die is rolled many times and the scores are noted. The table below shows the resulting frequency distribution.The die was rolled a total of 100 times.Write down an equation, in terms of and , for the total number of times the die was rolled. 10b. [2 marks] The mean score is 2.71.Using the mean score, write down a second equation in terms of and . 10c. [3 marks] Find the value of and of . 11a. [2 marks] The table below shows the distribution of test grades for 50 IB students at Greendale School.Calculate the mean test grade of the students; 11b. [1 mark] Calculate the standard deviation. 11c. [1 mark] Find the median test grade of the students. 11d. [2 marks] Find the interquartile range. 11e. [2 marks] A student is chosen at random from these 50 students.Find the probability that this student scored a grade 5 or higher. 11f. [3 marks] A second student is chosen at random from these 50 students.Given that the first student chosen at random scored a grade 5 or higher, find the probability that both students scored a grade 6. 11g. [2 marks] The number of minutes that the 50 students spent preparing for the test was normally distributed with a mean of 105 minutes and a standard deviation of 20 minutes.Calculate the probability that a student chosen at random spent at least 90 minutes preparing for the test. 11h. [2 marks] Calculate the expected number of students that spent at least 90 minutes preparing for the test. 12a. [3 marks] A sample of 120 oranges was tested for Vitamin C content. The cumulative frequency curve below represents the Vitamin C content, in milligrams, of these oranges.Giving your answer to one decimal place, write down the value of(i) ? ? the median level of Vitamin C content of the oranges in the sample;(ii) ? ? the lower quartile;(iii) ? ? the upper quartile. 12b. [3 marks] The minimum level of Vitamin C content of an orange in the sample was 30.1 milligrams. The maximum level of Vitamin C content of an orange in the sample was 35.0 milligrams.Draw a box-and-whisker diagram on the grid below to represent the Vitamin C content, in milligrams, for this sample. 13a. [4 marks] In the month before their IB Diploma examinations, eight male students recorded the number of hours they spent on social media.For each student, the number of hours spent on social media () and the number of IB Diploma points obtained () are shown in the following table.On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the -axis and 2 cm to represent 10 points on the -axis. 13b. [2 marks] Use your graphic display calculator to find(i) ? ? , the mean number of hours spent on social media;(ii) ? ? , the mean number of IB Diploma points. 13c. [2 marks] Plot the point ?on your scatter diagram and label this point M. 13d. [2 marks] Write down the value of , the Pearson’s product–moment correlation coefficient, for these data. 13e. [2 marks] Write down the equation of the regression line on for these eight male students. 13f. [2 marks] Draw the regression line, from part (e), on your scatter diagram. 13g. [2 marks] Ten female students also recorded the number of hours they spent on social media in the month before their IB Diploma examinations. Each of these female students spent between 3 and 30 hours on social media.The equation of the regression line y on x for these ten female students isAn eleventh girl spent 34 hours on social media in the month before her IB Diploma examinations.Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained. 13h. [1 mark] Write down a reason why this estimate is not reliable. 14a. [1 mark] A survey was conducted to determine the length of time, , in minutes, people took to drink their coffee in a café. The information is shown in the following grouped frequency table.Write down the total number of people who were surveyed. 14b. [1 mark] Write down the mid-interval value for the group. 14c. [2 marks] Find an estimate of the mean time people took to drink their coffee. 14d. [2 marks] The information above has been rewritten as a cumulative frequency table.Write down the value of and the value of . 14e. [4 marks] This information is shown in the following cumulative frequency graph.For the people who were surveyed, use the graph to estimate(i) ? ? the time taken for the first people to drink their coffee;(ii) ? ? the number of people who take less than minutes to drink their coffee;(iii) ? ? the number of people who take more than minutes to drink their coffee. 15a. [1 mark] A survey was carried out on a road to determine the number of passengers in each car (excluding the driver). The table shows the results of the survey.State whether the data is discrete or continuous. 15b. [1 mark] Write down the mode. 15c. [4 marks] Use your graphic display calculator to find(i) ? ? the mean number of passengers per car;(ii) ? ? the median number of passengers per car;(iii) ? ? the standard deviation. 16a. [4 marks] The table shows the distance, in km, of eight regional railway stations from a city centre terminus and the price, in , of a return ticket from each regional station to the terminus.Draw a scatter diagram for the above data. Use a scale of cm to represent km on the -axis and cm to represent on the -axis. 16b. [2 marks] Use your graphic display calculator to find(i) ? ? , the mean of the distances;(ii) ? ? , the mean of the prices. 16c. [1 mark] Plot and label the point on your scatter diagram. 16d. [3 marks] Use your graphic display calculator to find(i) ? ? the product–moment correlation coefficient, (ii) ? ? the equation of the regression line??on . 16e. [2 marks] Draw the regression line ?on on your scatter diagram. 16f. [3 marks] A ninth regional station is km from the city centre terminus.Use the equation of the regression line to estimate the price of a return ticket to the city centre terminus from this regional station. Give your answer correct to the nearest?. 16g. [1 mark] Give a reason why it is valid to use your regression line to estimate the price of this return ticket. 16h. [2 marks] The actual price of the return ticket is .Using your answer to part (f), calculate the percentage error in the estimated price of the ticket. 17a. [1 mark] The weights, in kg, of 60 adolescent females were collected and are summarized in the box and whisker diagram shown below.Write down the median weight of the females. 17b. [2 marks] Calculate the range. 17c. [1 mark] Estimate the probability that the weight of a randomly chosen female is more than 50 kg. 17d. [2 marks] Use the box and whisker diagram to determine if the mean weight of the females is less than the median weight. Give a reason for your answer.Printed for International School of Europe ? International Baccalaureate Organization 2019 International Baccalaureate? - Baccalauréat International? - Bachillerato Internacional? ................
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