IB Maths AA 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 2, calculatorEasy6 marks

The parking duration XX in hours, of a randomly selected vehicle at a car park is modelled by the probability density function

f(x)={14,0≤x≤4,0,otherwise.f(x)= \begin{cases} \frac14, & 0\leq x\leq 4,\\ 0, & \text{otherwise}. \end{cases}
(a)

Find the mean parking duration E(X)E(X) giving your answer in hours.

[2]
(b)

Determine Var⁡(X)\operatorname{Var}(X) giving your answer in hours squared.

[2]
(c)

The parking charge CC in dollars, is given by C=2+0.5XC=2+0.5X Hence find E(C)E(C) and Var⁡(C)\operatorname{Var}(C) giving appropriate units.

[2]

Question 2

Paper 2, calculatorEasy4 marks

A psychologist models scores on a test as a normally distributed random variable XX measured in points. Figure 1 shows two cumulative probabilities for this distribution.

20304050607080x (score, points)fX(x)P(X≤42)=0.20P(X≤58)=0.854258
(a)

Using a GDC, determine the zz-value corresponding to X=42X=42 Give your answer to four significant figures.

[1]
(b)

Using a GDC, determine the zz-value corresponding to X=58X=58 Hence use both zz-values to determine the mean and standard deviation of XX giving each answer to three significant figures.

[3]

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