A discrete random variable Y Y\,Y has a distribution that is approximately symmetric and bell-shaped, with mean 90 and variance 72. It is modelled by X∼N(90,72)X\sim N(90,72)X∼N(90,72).
Use a continuity correction to estimate P(80≤Y≤100)P(80\leq Y\leq100)P(80≤Y≤100).
State one reason why the quality of this approximation should be checked using the original distribution.