In a random sample of 50 students from a large university, all the students were between 18 and 20 years old. can we conclude that the entire population of students at the university is between 18 and 20 years old? explain.

Two angles are complementary. the large angle is 36 more than the smaller angle. what is the measure of the large angle?

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?

Larry wants to buy some carpeting for his living room. the length of the room is 4 times the width and the total area of the room is 16 square meters. what is the length of the living room