1. marisol is preparing a care package to send to her brother. the package will include a board game that weighs 4 pounds and several snack packs that each weigh ½ lb. the total weight of the care package must be less than 25 pounds. (a)write an inequality to model the situation. use x to stand for the number of snack packs she includes. (b) solve the inequality to find the maximum number of snack packs marisol can include in the package. (c) what is the maximum number of snack packs marisol can include in the package? give your answer in the form of a sentence.

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?