1. Study Habits (a) Randomly selected student’s scores would presumably be unrelated. (b) The mean of the difference: 120 – 105 = 15 points. The variance of the difference is 2009 so the standard deviation of the difference is 44.8219 points.

2. Study Habits We cannot find the probability based on only the mean and standard deviation. Many different distributions have the same mean and standard deviation. DO NOT ASSUME NORMAL!!!!

3. Swim Team State: What is the probability that the total team swim time is less than 220 seconds? Plan: Let T stand for the total team swim time and X1 be Wendy’s time, X2 be Jill’s time, X3 be Carmen’s time, and X4 be Latrice’s time. Then T = X1 + X2 + X3 + X4. The mean and variance are μT = 224.2 seconds and 30.89 seconds. This means that seconds. Since each individual’s time is approximately Normally distributed, that means that T is approximately Normally distributed.

4. Swim Team Putting this all together, we have that T has a standard deviation of 5.56. Thus, N(224.2, 5.56) distribution. Use this to find P(T < 220). Do: P(T < 220) = 0.2236. Conclude: There is approximately a 22% chance that the team’s swim time will be less than 220 seconds.