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 N ( μ , σ 2 ) .

* 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

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

P(X< 17) = 0.94

$\Rightarrow \frac{17-\mu }{\sigma }=1.554\dots$ (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]