Cindy wants to predict how much energy she will use to heat her home based on how cold it is outside. The table below shows the mean amount of gas per day (in cubic meters) that Cindy used each month and the average temperature that month (in degrees Celsius) for one heating season. Temperature (degrees Celsius) 0.00.00, point, 0 2.02.02, point, 0 4.54.54, point, 5 7.27.27, point, 2 10.010.010, point, 0 12.812.812, point, 8 Gas used (cubic meters) 22.022.022, point, 0 17.017.017, point, 0 16.716.716, point, 7 14.214.214, point, 2 12.012.012, point, 0 6.06.06, point, 0 All of the scatter plots below display the data correctly, but which one of them displays the data best? By convention, a good scatter plot uses a reasonable scale on both axes and puts the explanatory variable on the xxx-axis.

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?