A discrete count Y Y\,Y has mean 72 and variance 60. Its observed distribution is unimodal and approximately symmetric, so it is modelled by X∼N(72,60)X\sim N(72,60)X∼N(72,60).
Use a continuity correction to estimate P(Y≥85)P(Y\geq85)P(Y≥85).
Explain why the stated shape supports the Normal approximation.
Give one reason why the approximation may still be inaccurate in the upper tail.