The weight of adult female giraffes has a normal distribution with mean 830 kg and standard deviation 120 kg.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [4] P(t < 700) = P (z < (700-830) / 120) = P(z < -1.083). Using ± standardisation formula, no continuity correction, not σ² or √σ M1 = 1 - 0.8606. Appropriate area Φ from standardisation formula P(z<....) in final probability solution, (<0.5 if z is –ve, >0.5 if z is +ve) M1 = 0.1394. Correct final probability rounding to 0.139 A1 Expected number of female adults = 430 × their 0.1394 = 59.9 So 59 or 60. FT their 3 or 4 SF probability, rounded or truncated to integer B1
2. [3] P(giraffe < 830+w) = 95% so z = 1.645. ±1.645 seen (critical value) B1 (830+w)-830 / 120 = w / 120 = 1.645. An equation using the standardisation formula with a z-value (not 1 – z), condone σ² or √σ not 0.8519, 0.8289 M1 w = 197. Correct answer A1
3. [3] P(male > 950) = 0.834, so z = -0.97. ±0.97 seen B1 (950-1190) / σ = -0.97. Using ± standardisation formula, condone continuity correction, σ² or √σ, condone equating with non z-value not 0.834, 0.166 M1 σ = 247. Condone -σ = -247. www. A1