Aand b are two events. let p(a)=0.3 , p(b)=0.8 , and p(a and b)=0.24 . which statement is true? (a). a and b are not independent events because p(a|b)=p(a) and p(b|a)=p(b) . (b). a and b are not independent events because p(a|b)=p(b) and p(b|a)=p(a) . (c). a and b are independent events because p(a|b)=p(b) and p(b|a)=p(a) . (d). a and b are not independent events because p(a|b)≠p(a) .

Acompany produces packets of soap powder labeled “giant size 32 ounces.” the actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. to avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. to avoid losing money, it labels the top 5% (the heaviest 5%) overweight. how heavy does a box have to be for it to be labeled overweight?