A survey was conducted to determine how many movies were seen in one month among the 26 students in Mrs. Hampton’s sixth-grade class. The results are shown in the dot plot below. a) Calculate the measures of center for the data in the dot plot, rounding your answers to the nearest tenths place. Show how you determined your answer. (2 points)

b) Are there any overall patterns in the data set? Striking deviations? Use mathematical reasoning to justify your answer. (2 points)

c) Calculate the measures of spread for Mrs. Hampton’s class data. Justify your response by describing the process used to find each measure. (2 points)

d) Which is a better measure of spread: range or interquartile range? Why? (2 points)

e) What does the value of the mean absolute deviation tell you about the spread of the data? (2 points)

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?