| Date | May 2018 | Marks available | 2 | Reference code | 18M.2.hl.TZ2.3 |
| Level | HL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
The random variable X has a normal distribution with mean μ = 50 and variance σ 2 = 16 .
Sketch the probability density function for X, and shade the region representing P(μ − 2σ < X < μ + σ).
[2]
a.
Find the value of P(μ − 2σ < X < μ + σ).
[2]
b.
Find the value of k for which P(μ − kσ < X < μ + kσ) = 0.5.
[2]
c.
Markscheme
normal curve centred on 50 A1
vertical lines at \(x\) = 42 and \(x\) = 54, with shading in between A1
[2 marks]
a.
P(42 < X < 54) (= P(− 2 < Z < 1)) (M1)
= 0.819 A1
[2 marks]
b.
P(μ − kσ < X < μ + kσ) = 0.5 ⇒ P(X < μ + kσ) = 0.75 (M1)
k = 0.674 A1
Note: Award M1A0 for k = −0.674.
[2 marks]
c.
Examiners report
[N/A]
a.
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b.
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c.
