Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.
The histogram in Figure 1 shows the response times, seconds, for 32 service calls. The standard deviation of these response times is seconds.
State the modal class and estimate the mean response time.
For each response time a service index measured in index units, is defined by
Hence, using your estimate from part (a), determine the estimated mean and the standard deviation of
A grower records the irrigation time, hours, and the harvested mass, kg, for five greenhouse beds.
| 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|
| 2 | 3 | 3 | 5 | 6 |
Determine, giving your working, the equation of the regression line of on in the form
Hence estimate the harvested mass when the irrigation time is 4 hours.
The grower wants to estimate the irrigation time from a harvested mass of kg. A trainee rearranges the equation from part (a) and obtains an estimate of 4 hours. Explain whether this is a justified use of a regression line.
A probability tree models the results of a medical study of a risk factor and a disease A person is selected at random from the population. The probabilities on the second set of branches are conditional on the outcome at the first set of branches.
Find the probability that a randomly selected person has both and
Hence determine the probability that a randomly selected person has
Hence determine the probability that a person has given that they have Give your answer exactly, and state whether more than half of the people with have
A health service records whether each of 300 participants has a risk factor and whether each is diagnosed with a disease Figure 1 shows the results.
A report notes that more participants diagnosed with had than did not have and concludes that diagnosis is more likely among participants with
State the definition of in terms of and
Use Figure 1 to calculate
In light of your answer to (b), test whether and are independent and assess the report’s conclusion.
The graph in Figure 1 shows the probability density function, of a continuous random variable
Write down as a piecewise function.
Determine
Hence determine
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