IB Maths AI HL 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.

Question 1

Paper 2Medium5 marks

At a parcel centre, XX is the excess handling time, in minutes, for a randomly selected parcel. Figure 1 shows the probability distribution of XX

012300.10.20.30.40.50.6Excess handling time, x (min)P(X=x)0.200.500.30
(a)

Calculate E(X)\mathrm{E}(X) and Var(X)\mathrm{Var}(X)

[3]
(b)

For a parcel with excess handling time XX the additional handling charge YY in AUD, is modelled by Y=3X+2Y=3X+2 Hence determine E(Y)\mathrm{E}(Y) and Var(Y)\mathrm{Var}(Y)

[2]

Question 2

Paper 1Medium6 marks

A parcel-delivery company defines its daily forecast error as

actual number of parcels−forecast number of parcels.\text{actual number of parcels}-\text{forecast number of parcels}.

A random sample of 16 independent days has a mean forecast error of 18.4 parcels and a sample standard deviation of 12.0 parcels. The daily forecast errors may be modelled by a normal population, whose standard deviation is unknown.

(a)

State which distribution should be used to construct a confidence interval for the population mean forecast error, μ\mu

[1]
(b)

Calculate a 95% confidence interval for μ\mu Give both endpoints to one decimal place.

[3]
(c)

The planning director claims that the forecasts are unbiased, so that μ=0\mu=0 Use your interval to comment on this claim and state the direction of any bias indicated.

[2]

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