A match of Hoop Fever gives each player 60 seconds to make as many baskets as possible. Morgan and Tim play head-to-head every Tuesday. Suppose that M = the number of baskets made by Morgan in a randomly selected match follows an approximately Normal distribution with mue_M = 39.8 and sigma_M = 5.7. Suppose that T = the number of baskets made by Tim in a randomly selected match follows an approximately Normal distribution with mue_T = 31.2 and sigma_T = 10.3. Assume that these two random variables are independent and define D = M - T. a. Describe the distribution of D. b. What is the probability that Morgan will make more baskets than Time in a randomly selected match?

Q3 A mixed-model assembly line has eight stations. Average cycle time is 15 mimutes, but times vary due to model type and natural randomness. The estimated standard deviation of processing time in a station is 4.5 minutes. Estimate the production rate for the asynchronous line if no buffer is allowed.

Suppose a professor uses a normal distribution to assign grades in her math class. • She assigns an A to students scoring more than 1.9 standard deviations above the mean. • She assigns an F to students scoring more than 2.2 standard deviations below the mean. She assigns a B to students who Score between 1 and 1.9 standard deviations above the mean. • She assigns a D to students who Score between 1.2 and 2.2 standard deviations below the mean. • All other students get a C. Use the Cumulative Z-Score Table to answer the following questions. The Z-Score Table can be found below by selecting "Read". Write your answer as a percent using 2 decimal places. What percent of the class receives each grade assuming the scores are normally distributed? Hint % will recieve an A % will recieve a B % will recieve a C % will recieve a D % will recieve an F

4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'st