IB Maths AA SL AA 4.4 Probability distributions 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 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]

Question 2

Paper 1, no calculatorHard6 marks

In a production run, the number of packets with faulty seals is modelled by $X\sim B(n,p)$ where $n$ and $p$ are unknown. The mean of $X$ is $3$ and its variance is $2.1$

(a)

Determine $n$ and $p$

[4]

(b)

In a separate check, an inspector selects 10 packets without replacement from a lot of 20 packets, of which exactly 6 have faulty seals. A supervisor uses the values of $n$ and $p$ from part (a) to model the number of faulty packets in the check. Comment on whether this is appropriate.

[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