A-LevelMathematicsProbability and statistics9709/63 · May/June 2017 · Q46 Marks
The random variable X has the distribution N(μ, σ²), where μ = 1.5σ. A random value of X is chosen. Find the probability that this value of X is greater than 0.
- (a)The random variable X has the distribution N(μ, σ²), where μ = 1.5σ. A random value of X is chosen. Find the probability that this value of X is greater than 0.[3]
- (b)The life of a particular type of torch battery is normally distributed with mean 120 hours and standard deviation s hours. It is known that 87.5% of these batteries last longer than 70 hours. Find the value of s.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [M1] P(x > 0) = P(z > ±(0 - μ)/σ) or P(z > -1.5σ/σ) Standardising, in terms of μ and/or σ with 0 - .... in numerator, no continuity correction, no √
- [A1] = P(z > -1.5) Obtaining z value of ±1.5 by eliminating μ and σ, SOI
- [A1] = 0.933
- [B1] z = -1.151 ± z value rounding to 1.1 or 1.2
- [M1] -1.151 = (70-120)/s ± Standardising (using 70) equated to a z-value, no cc, no squaring, no √
- [A1] σ = 43.4 or 43.5
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