A study was conducted to determine if consumers are more likely to choose a vice product​ (e. g., a candy​ bar) when their arm is flexed​ (as when carrying a shopping​ basket) than when their arm is extended​ (as when pushing a shopping​ cart). The study measured choice scores​ (on a scale of 0 to​ 100, where higher scores indicate a greater preference for vice​ options) for consumer shopping under each of the two conditions. The average choice score for consumers with a flexed arm was ​, while the average for consumers with an extended arm was . For both​ conditions, assume that the standard deviation of the choice scores is . Also assume that both distributions are approximately normally distributed. Complete parts a. and b.