IB Maths AA 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, no calculator Paper 2, calculator

Difficulty

Easy Medium Hard

Question 1

Paper 2, calculatorMedium6 marks

The waiting times, in minutes, for a sample of eight customers at a repair desk were

12, 14, 14, 16, 18, 19, 21, 26.

(a)

Use your GDC to determine the sample mean and sample standard deviation, correct to three significant figures.

[2]

(b)

Hence find the sample variance, correct to three significant figures.

[1]

(c)

For a later report, 3 minutes is subtracted from every waiting time in the sample. A supervisor claims that the standard deviation will therefore also decrease by 3 minutes.

Determine the new sample mean and standard deviation, and comment on the supervisor’s claim.

[3]

A courier company records the delivery times for 40 trips on each of two routes. Figure 1 shows box-and-whisker diagrams for the two sets of times. For this comparison, use the median to represent typical delivery time and the interquartile range (IQR) to represent consistency.

(a)

State the median delivery time for each route.

[2]

(b)

Calculate the IQR for each route.

[2]

(c)

Recommend a route if the company wants both a shorter typical delivery time and more consistent delivery times. Justify your recommendation using the medians and IQRs.

[2]

Question 3

Paper 1, no calculatorMedium8 marks

A machine produces metal pins whose lengths are modelled by a normal distribution with mean $42$ mm and standard deviation $3$ mm.

For this question, use the facts that approximately $68\%$ $95\%$ and $99.7\%$ of values lie within one, two and three standard deviations of the mean, respectively.

(a)

Estimate the percentage of pins with lengths between $39$ mm and $45$ mm.

[1]

(b)

Hence, estimate the percentage of pins with lengths between $39$ mm and $48$ mm.

[3]

(c)

A batch contains $800$ pins. Hence, estimate the number of pins in the batch with lengths between $39$ mm and $48$ mm.

[2]

(d)

A pin has length $51$ mm. Estimate the percentage of pins with lengths greater than $51$ mm, giving your reasoning.

[2]

The best questions are still waiting

Unlock every question in this topic, then type, photograph or draw your answer and have it marked against the markscheme. Find out where you are dropping marks.

Unlock all questions Compare Student and Student Plus