DP Mathematics: Applications and Interpretation Questionbank

Find the value of $a$.

Write down the value of the median distance in kilometres (km).

Find the value of $b$.

Find $m$.

The first $150$ athletes that completed the race won a prize.

Given that an athlete took between $22$ and $m$ minutes to complete the $5 \text{km}$ race, calculate the probability that they won a prize.

Find the probability that it will take Fiona between $15$ minutes and $30$ minutes to walk to the bus stop.

Find $\sigma$.

Find the probability that the bus journey takes less than $45$ minutes.

Find the probability that Fiona will arrive on time.

This year, Fiona will go to school on $183$ days.

Calculate the number of days Fiona is expected to arrive on time.

Write down the modal group for these data.

Use your graphic display calculator to find an estimate of the standard deviation of the weights of mangoes from this harvest.

On the grid below, draw a histogram for the data in the table.

Find the height of Flower $\text{B}$.

Using this information, write down an equation in $p$ and $q$.

Write down a second equation in $p$ and $q$.

Using your answers to parts (b) and (c), find the height of Flower $\text{A}$.

Using your answers to parts (b) and (c), find the height of Flower $\text{D}$.

the mean.

the mode.

the standard deviation.

Find the minimum score needed to obtain a grade $5$.

Find the median of the scores obtained.

Find an expression for $a$ in terms of $b$.

Find the number of students who obtained a grade $5$.

Find the lower quartile of the weights of the sacks of potatoes.

The sacks of potatoes are transported in crates. There are $10$ sacks in each crate and the weights of the sacks of potatoes are independent of each other.

Find the probability that the total weight of the sacks of potatoes in a crate exceeds $500 \text{kg}$.

Find the probability that a sack is under its labelled weight.

With reference to the box and whisker diagrams, state one aspect that may support the researcher’s opinion and one aspect that may counter it.

the upper quartile.

the interquartile range.

State whether the data is discrete or continuous.

the mean mark.

the standard deviation of the marks.

It was not possible to ask every person in the school, so the Headmaster arranged the student names in alphabetical order and then asked every 10th person on the list.

Identify the sampling technique used in the survey.

Find the value of $k$.

interquartile range of the reaction times.

Find the estimated number of teenagers who have a reaction time greater than $0.4$ seconds.

Determine the $90\text{th}$ percentile of the reaction times from the cumulative frequency graph.

Write down the value of $b$.

Write down the modal class from the table.

Use your graphic display calculator to find an estimate of the mean reaction time.

Suggest how, if at all, the estimated mean and estimated median reaction times will change if the errors are corrected. Justify your response.

Write down the value of $a$.

Find the value of p.

Find μ, the expected value of X.

Find P(X > μ).

Using this distribution model, find .

Using this distribution model, find the standard deviation of $X$.

an estimate for the mean number of emails received per working day.

an estimate for the standard deviation of the number of emails received per working day.

Give one piece of evidence that suggests Willow’s Poisson distribution model is not a good fit.

Suppose that the probability of Archie receiving more than 10 emails in total on any one day is 0.99. Find the value of λ.

Now suppose that Archie received exactly 20 emails in total in a consecutive two day period. Show that the probability that he received exactly 10 of them on the first day is independent of λ.

Show that $\text{P}(X=3)=0.001$ and $\text{P}(X=4)=0.0027$.

Find the values of the constants $a$ and $b$.

Deduce that $\frac{\text{P}(X=n)}{\text{P}(X=n-1)}=\frac{0.9(n-1)}{n-3}$ for $n>3$.

(i)     Hence show that $X$ has two modes $m_1$ and $m_2$.

(ii)     State the values of $m_1$ and $m_2$.

Determine the minimum value of $x$ such that the probability Kati receives at least one free gift is greater than 0.5.

the standard deviation.

Find the value of the interquartile range.

One student sent k text messages, where k > 11 . Given that k is an outlier, find the least value of k.

Write down the number of employees who worked 50 hours or less.

Find the amount of money an employee earned for working 40 hours;

Find the mean number of hours spent browsing the Internet.

During week 2, the students worked on a major project and they each spent an additional five hours browsing the Internet. For week 2, write down

(i)     the mean;

(ii)     the standard deviation.

During week 3 each student spent 5% less time browsing the Internet than during week 1. For week 3, find

(i)     the median;

(ii)     the variance.

(i)     Find the number of students who spent between 25 and 30 hours browsing the Internet.

(ii)     Given that 10% of the students spent more than k hours browsing the Internet, find the maximum value of $k$.

For the students in this group write down the median age.

Draw a box-and-whisker diagram, for these students’ ages, on the following grid.

Find the value of x.

Find the standard deviation

Find the interquartile range.

Write down the mid-interval value for the 100 < x ≤ 150 group.

On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours on the $x$-axis and 2 cm to represent 10 points on the $y$-axis.

(i)     $\overline{x}$, the mean number of hours spent on social media;

(ii)     $\overline{y}$, the mean number of IB Diploma points.

Plot the point $(\overline{x},\overline{y})$ on your scatter diagram and label this point M.

Write down the equation of the regression line $y$ on $x$ for these eight male students.

Draw the regression line, from part (e), on your scatter diagram.

Use the given equation of the regression line to estimate the number of IB Diploma points that this girl obtained.

Write down a reason why this estimate is not reliable.

State the alternative hypothesis.

Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.

Write down the number of degrees of freedom.

Write down the χ² statistic.

Write down the associated p-value.

State, with a reason, whether you would reject the null hypothesis.

Write down the probability that this flight arrived on time.

Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km.

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.

Calculate the mean test grade of the students;

Calculate the standard deviation.

Find the median test grade of the students.

Find the interquartile range.

Find the probability that this student scored a grade 5 or higher.

Given that the first student chosen at random scored a grade 5 or higher, find the probability that both students scored a grade 6.

Calculate the probability that a student chosen at random spent at least 90 minutes preparing for the test.

Calculate the expected number of students that spent at least 90 minutes preparing for the test.

Write down the mid-interval value for 10 ≤ t < 15.

Write down the total number of customers in terms of k.

Find the number of buses that travelled a distance between 15000 and 20000 kilometres.

Use the cumulative frequency curve to find the median distance.

Use the cumulative frequency curve to find the lower quartile.

Use the cumulative frequency curve to find the upper quartile.

Hence write down the interquartile range.

Write down the percentage of buses that travelled a distance greater than the upper quartile.

Find the number of buses that travelled a distance less than or equal to 12 000 km.

Find the value of m.

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.

State whether $N$ is a discrete or a continuous variable.

Write down, for $N$, the modal class;

Write down, for $N$, the mid-interval value of the modal class.

Use your graphic display calculator to estimate the mean of $N$;

Use your graphic display calculator to estimate the standard deviation of $N$.

Find the expected frequency of students choosing the Science category and obtaining 31 to 40 correct answers.

Write down the null hypothesis for this test;

Write down the number of degrees of freedom.

Write down the $p$-value for the test;

Write down the ${\chi }^2$ statistic.

State the result of the test. Give a reason for your answer.

Write down an equation, in terms of $x$ and $y$, for the total number of times the die was rolled.

Using the mean score, write down a second equation in terms of $x$ and $y$.

Find the value of $x$ and of $y$.

Write down the total number of people, from this group, who are pet owners.

Write down the modal number of pets.

For these data, write down the median number of pets.

For these data, write down the lower quartile.

For these data, write down the upper quartile.

Write down the ratio of teenagers to non-teenagers in its simplest form.

State the null hypothesis.

State the alternative hypothesis.

Write down the number of degrees of freedom for this test.

Calculate the expected number of teenagers that prefer cats.

State the conclusion for this test. Give a reason for your answer.

The health inspector visits two school cafeterias. She inspects the same number of meals at each cafeteria. The data is shown in the following box-and-whisker diagrams.

Meals prepared in the school cafeterias are required to have less than 10 grams of sugar.

State, giving a reason, which school cafeteria has more meals that do not meet the requirement.

On the following diagram, shade the region representing the probability that the price of a kilogram of tomatoes, chosen at random, will be higher than 3.22 euro.

Find the price that is two standard deviations above the mean price.

Find the probability that the price of a kilogram of tomatoes, chosen at random, will be between 2.00 and 3.00 euro.

To stimulate reasonable pricing, the city offers a free permit to the sellers whose price of a kilogram of tomatoes is in the lowest 20 %.

Find the highest price that a seller can charge and still receive a free permit.

Draw a box-and-whisker diagram on the grid below to represent the Vitamin C content, in milligrams, for this sample.

State whether the weight of the eggs is a continuous or discrete variable.

Write down the modal grade of the eggs.

Use your graphic display calculator to find an estimate for the standard deviation of the weight of the eggs.

The mean weight of these eggs is 64.9 grams, correct to three significant figures.

Use the table and your answer to part (c) to find the smallest possible number of eggs that could be within one standard deviation of the mean.