Question 1 - A-Level Maths

CAIE S1 2016 June — Question 1 3 marks

Exam Board	CAIE
Module	S1 (Statistics 1)
Year	2016
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Normal Distribution
Type	Find standard deviation from probability
Difficulty	Moderate -0.3 This is a straightforward inverse normal distribution problem requiring students to use standard normal tables (or calculator) to find the z-score corresponding to P(Z > z) = 0.15, then apply the standardization formula to solve for σ. It's slightly easier than average as it's a single-step application of a standard technique with no conceptual complications.
Spec	2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation

1 The height of maize plants in Mpapwa is normally distributed with mean 1.62 m and standard deviation \(\sigma \mathrm { m }\). The probability that a randomly chosen plant has a height greater than 1.8 m is 0.15 . Find the value of \(\sigma\).

Show mark scheme Show mark scheme source

Question 1:

Answer	Marks	Guidance
Answer	Marks	Guidance
\(z = 1.037\)	B1	Rounding to 1.04
\(1.037 = \frac{1.8 - 1.62}{\sigma}\)	M1	Standardising attempt; allow cc no sq rt; must have a z-value i.e. not 0.8023 or 0.5596
\(\sigma = 0.18/1.037 = 0.174\)	A1 [3]

## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $z = 1.037$ | B1 | Rounding to 1.04 |
| $1.037 = \frac{1.8 - 1.62}{\sigma}$ | M1 | Standardising attempt; allow cc no sq rt; must have a z-value i.e. not 0.8023 or 0.5596 |
| $\sigma = 0.18/1.037 = 0.174$ | A1 [3] | |

---

Show LaTeX source

1 The height of maize plants in Mpapwa is normally distributed with mean 1.62 m and standard deviation $\sigma \mathrm { m }$. The probability that a randomly chosen plant has a height greater than 1.8 m is 0.15 . Find the value of $\sigma$.

\hfill \mbox{\textit{CAIE S1 2016 Q1 [3]}}

This paper (7 questions)

View full paper

Q1 3 Q2 5 Q3 5 Q4 6 Q5 9 Q6 11 Q7 11