Standard +0.3 This is a standard inverse normal distribution problem requiring students to set up two equations using z-scores from given percentages (20% and 71.9% correspond to z ≈ 0.84 and z ≈ -0.58) and solve simultaneously for μ and σ. While it involves multiple steps, the technique is routine for S1 and requires no novel insight—just systematic application of the inverse normal method.
4 It is known that 20\% of male giant pandas in a certain area weigh more than 121 kg and \(71.9 \%\) weigh more than 102 kg . Weights of male giant pandas in this area have a normal distribution. Find the mean and standard deviation of the weights of male giant pandas in this area.
\(z = 0.842 = \left(\frac{121-\mu}{\sigma}\right)\), so \(0.842\sigma = 121-\mu\)
B1
\(\pm 0.842\) seen but B0 if \(1\pm 0.842\) oe seen
M1
One appropriate standardisation equation with a \(z\)-value, \(\mu\), \(\sigma\) and 121 or 102, condone continuity correction. Not \(0.158, 0.42,\ldots\)
\(z = -0.58 = \left(\frac{102-\mu}{\sigma}\right)\), so \(-0.58\sigma = 102-\mu\)
B1
\(\pm 0.58(0)\) seen but B0 if \(1\pm 0.58\) oe seen
Solving
M1
Correct algebraic elimination of \(\mu\) or \(\sigma\) from \(their\) two simultaneous equations to form an equation in one variable, condone 1 numerical slip
\(\sigma = 13.4\), \(\mu = 110\)
A1
If M0A0 scored, SC B1 can be awarded for both answers correct. Consistent use of \(\sigma^2\) or \(\sqrt{\sigma}\) throughout apply MR penalty to A or SC B mark
## Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $z = 0.842 = \left(\frac{121-\mu}{\sigma}\right)$, so $0.842\sigma = 121-\mu$ | B1 | $\pm 0.842$ seen but B0 if $1\pm 0.842$ oe seen |
| | M1 | One appropriate standardisation equation with a $z$-value, $\mu$, $\sigma$ and 121 **or** 102, condone continuity correction. Not $0.158, 0.42,\ldots$ |
| $z = -0.58 = \left(\frac{102-\mu}{\sigma}\right)$, so $-0.58\sigma = 102-\mu$ | B1 | $\pm 0.58(0)$ seen but B0 if $1\pm 0.58$ oe seen |
| Solving | M1 | Correct algebraic elimination of $\mu$ or $\sigma$ from $their$ two simultaneous equations to form an equation in one variable, condone 1 numerical slip |
| $\sigma = 13.4$, $\mu = 110$ | A1 | If M0A0 scored, **SC B1** can be awarded for both answers correct. Consistent use of $\sigma^2$ or $\sqrt{\sigma}$ throughout apply **MR** penalty to A or SC B mark |
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4 It is known that 20\% of male giant pandas in a certain area weigh more than 121 kg and $71.9 \%$ weigh more than 102 kg . Weights of male giant pandas in this area have a normal distribution. Find the mean and standard deviation of the weights of male giant pandas in this area.\\
\hfill \mbox{\textit{CAIE S1 2019 Q4 [5]}}