The following box-and-whisker plot shows the number of text messages sent by students in a school on a particular day.

A large school has students from Year 6 to Year 12. A group of $80$ students in Year 12 were randomly selected and surveyed to find out how many hours per week they each spend doing homework. Their results are represented by the following cumulative frequency graph.

This same information is represented by the following table.

There are $320$ students in Year 12 at this school.

SpeedWay airline flies from city $A$ to city $B$. The flight time is normally distributed with a mean of 260 minutes and a standard deviation of 15 minutes. A flight is considered late if it takes longer than 275 minutes.

The flight is considered to be on time if it takes between $m$ and 275 minutes. The probability that a flight is on time is 0.830.

During a week, SpeedWay has 12 flights from city $A$ to city $B$. The time taken for any flight is independent of the time taken by any other flight.

Box 1 contains 5 red balls and 2 white balls. Box 2 contains 4 red balls and 3 white balls.

A bakery makes two types of muffins: chocolate muffins and banana muffins.

The weights, $C$ grams, of the chocolate muffins are normally distributed with a mean of $62 \, \text{g}$ and standard deviation of $2.9 \, \text{g}$.

The weights, $B$ grams, of the banana muffins are normally distributed with a mean of $68 \, \text{g}$ and standard deviation of $3.4 \, \text{g}$.

Each day $60\%$ of the muffins made are chocolate.

On a particular day, a muffin is randomly selected from all those made at the bakery.The machine that makes the chocolate muffins is adjusted so that the mean weight of the chocolate muffins remains the same but their standard deviation changes to $\sigma \, \text{g}$. The machine that makes the banana muffins is not adjusted. The probability that the weight of a randomly selected muffin from these machines is less than $61 \, \text{g}$ is now $0.157$.

A data set consisting of $16$ test scores has mean $14.5$. One test score of $9$ requires a second marking and is removed from the data set. Find the mean of the remaining $15$ test scores.

Applicants for a job had to complete a mathematics test. The time they took to complete the test is normally distributed with a mean of 53 minutes and a standard deviation of 16.3. One of the applicants is chosen at random.

For 11% of the applicants it took longer than ${k}$ minutes to complete the test.

There were 400 applicants for the job.

A company performs an experiment on the efficiency of a liquid that is used to detect a nut allergy. A group of 60 people took part in the experiment. In this group 26 are allergic to nuts. One person from the group is chosen at random.

A second person is chosen from the group.

When the liquid is added to a person’s blood sample, it is expected to turn blue if the person is allergic to nuts and to turn red if the person is not allergic to nuts. The company claims that the probability that the test result is correct is 98% for people who are allergic to nuts and 95% for people who are not allergic to nuts. It is known that 6 in every 1000 adults are allergic to nuts. This information can be represented in a tree diagram.

An adult, who was not part of the original group of 60, is chosen at random and tested using this liquid.

The liquid is used in an office to identify employees who might be allergic to nuts. The liquid turned blue for 38 employees.

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 $0 \leq t < 20$.

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.

Two unbiased tetrahedral (four-sided) dice with faces labelled 1, 2, 3, 4 are thrown and the scores recorded. Let the random variable T be the maximum of these two scores. The probability distribution of T is given in the following table.