A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2017 · Q713 Marks
The lengths, in centimetres, of middle fingers of women in Raneland have a normal distribution with mean u and standard deviation σ. It is found that 25% of these women have fingers longer than 8.8 cm and 17.5% have fingers shorter than 7.7 cm.
- (a)(i)Find the values of u and σ.[5]
- (a)(ii)The lengths, in centimetres, of middle fingers of women in Snoland have a normal distribution with mean 7.9 and standard deviation 0.44. A random sample of 5 women from Snoland is chosen. Find the probability that exactly 3 of these women have middle fingers shorter than 8.2 cm.[5]
- (b)The random variable X has a normal distribution with mean equal to the standard deviation. Find the probability that a particular value of X is less than 1.5 times the mean.[3]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.
- [B1] ±0.674 seen
- [B1] ±0.935 seen (condone ±0.934)
- [M1] An eqn with a z-value, μ and σ allow sq rt, sq cc
- [M1] sensible attempt to eliminate μ or σ by substitution or subtraction
- [A1] correct answers (from -0.935) (σ = 0.684, μ = 8.34)
- [M1] Standardising no cc no sq rt no sq (for Z value)
- [M1] Correct area ie Φ, final solution (for probability p)
- [A1] Correct prob rounding to 0.752 (for p)
- [M1] Binomial Cₓ powers summing to 5, any p, ∑p = 1
- [A1] = 0.261
- [*M1] standardising with μ and σ (σ may be replaced by μ)
- [DM1] just one variable
- [A1] = 0.692
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