A soap maker manufactures bars of soap in three different sizes: 3. 15-ounce, 4-ounce, and 6-ounce bars. The company randomly surveyed people at a number of supermarkets across the country about which size bar they typically buy. Survey results showed that 40% buy the 3. 15-ounce bar, 50% prefer the 4-ounce bar, and 10% purchase the 6-ounce bar. If the company sells 62,500 bars of soap each day, approximately how many 3. 15-ounce bars should they sell per day across the country?.

(a) (8%) compute the probability of an even integer among the 100 integers 1! , 2! , 3! , until 100! (here n! is n factorial or n*(n-1)*(n-2) *… 1) (b) (16%) compute the probability of an even integer among the 100 integers: 1, 1+2, 1+2+3, 1+2+3+4, …., 1+2+3+… + 99, and 1+2+3+… + 100

Under normal conditions, 1.5 feet of snow will melt into 2 inches of water. during a winter season high in the mountains, 301 feet of snow fell. how many inches of water will there be when the snow melts?

Four airplanes carrying a total of 400 passengersarrive at the detroit airport. the airplanes carry, respectively,50, 80, 110, and 160 passengers.a) one of the 400 passengers is selected uniformly at random.let x denote the number of passengers that were on theairplane carrying the randomly selected passenger. find var(x)for x as given in the problemb) one of the 4 airplane drivers is also selected uniformly atrandom. let y denote the number of passengers on the chosen driver’s airplane. find var(y) for y as given in the problem