IB Maths AI SL Topic 4: Statistics and probability questions

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.

Paper

Paper 1 Paper 2

Difficulty

Easy Medium Hard

Question 1

Paper 1Hard8 marks

At a cereal plant, the mass $X$ in grams, of a randomly selected bag is modelled by a normal distribution with mean $502$ g and standard deviation $4.8$ g. A bag is accepted if its mass is at least $500$ g.

The machine can be adjusted by adding the same amount $d$ grams to the mass of every bag. This adjustment does not change the standard deviation.

(a)

Write down the interval that contains approximately $68\%$ of the bag masses at the current setting.

[1]

(b)

Use your GDC to find the probability that a randomly selected bag is accepted at the current setting. Give your answer to four significant figures.

[2]

(c)

The manager requires at least $97.5\%$ of the bags to be accepted. Using your answer to (b), state whether the current setting meets this requirement. Determine the smallest value of $d$ that meets the requirement. Give your answer to three significant figures.

[5]

Question 2

Paper 1Medium6 marks

During fieldwork, 40 quadrats were examined in each of three habitat types. In each quadrat, the fieldworkers recorded whether moths were detected. Figure 1 shows their results.

(a)

State the null hypothesis, $H_0$ and the alternative hypothesis, $H_1$ for a test of whether moth detection and habitat type are independent.

[2]

(b)

Assuming $H_0$ is true, calculate the expected frequency of quadrats in habitat B in which moths are detected. Give your answer to 3 significant figures.

[1]

(c)

Use a GDC to carry out an appropriate test of independence using the frequencies in Figure 1. Give the $\chi^2$ statistic and the $p$ -value, each to 3 significant figures.

[2]

(d)

Hence state the conclusion of the test at the 5% significance level, in the context of the fieldwork.

[1]

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