18N.2.AHL.TZ0.H_3

pestleMathematicsAAHLPaper 218N· sl-4-9-normal-distribution-and-calculationssource ↗

It is known that 56 % of Infiglow batteries have a life of less than 16 hours, and 94 % have a life less than 17 hours. It can be assumed that battery life is modelled by the normal distribution ${\text{N}}\left( {\mu ,\,\,{\sigma ^2}} \right)$ .

Find the value of $\mu$ and the value of $\sigma$ .

[6]

Find the probability that a randomly selected Infiglow battery will have a life of at least 15 hours.

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

use of inverse normal (implied by ±0.1509… or ±1.554…) (M1)

P(X < 16) = 0.56

$\Rightarrow \frac{{16 - \mu }}{\sigma } = 0.1509 \ldots$ (A1)

P(X < 17) = 0.94

$\Rightarrow \frac{{17 - \mu }}{\sigma } = 1.554 \ldots$ (A1)

attempt to solve a pair of simultaneous equations (M1)

$\mu$ = 15.9, $\sigma$ = 0.712 A1A1

[6 marks]

correctly shaded diagram or intent to find P(X ≥ 15) (M1)

= 0.895 A1

Note: Accept answers rounding to 0.89 or 0.90. Award M1A0 for the answer 0.9.

[2 marks]

Examiners’ report

[N/A]