Central Sports and United County Health are two local youth basketball leagues. Last season, Lucy scored a total of $551$ points in Central Sports and Rachel

scored a total of $620$ points in United County Health.

Last season, the total points scored per player in Central Sports had a population mean of $411$ points and a standard deviation of $74$ points, and the total

points scored per player in United County Health had a population mean of $549$ points and a standard deviation of $61$ points. For each league, the distribution

of total points scored last season per player was clearly skewed $($not approximately symmetric$).$

$($a$)$ Find the $z-$scores of Lucy's total points scored last season as a player in Central Sports and Rachel's total points scored

last season as a player in United County Health. Round your answers to two decimal places.

$z-$score of Lucy's total points scored last season:

$z-$score of Rachel's total points scored last season:$($b$)$ Relative to her population, who was the higher scorer?

Choose the best answer based on the $z-$scores of the two players.

Lucy

Rachel

It is unclear who was the higher scorer relative to her population