7. Run some probabilities, discuss in the group forum as needed: a) What is the probability that a single randomly chosen value (from 1 to 100) would be over 55? [Note that this is a uniform distribution, so don't use the NormalCdf command] b) What is the probability that the mean of a group of 5 randomly chosen values (from 1 to 100) would be over 55? [Note the population SD is 29.01, and that sample means are approximately Normally distributed, so the NormalCdf command is now appropriate, but adjust your SD to reflect a sample size of 5] c) Look over your group results - what proportion of your group's samples of 5 have a mean over 55? Is this close to your prediction in (b)? d) What is the probability that the mean of a group of 20 randomly chosen values (from 1 to 100) would be over 55 (adjust your SD to reflect a sample size of 20)? e) Look over your group results - what proportion of your group's samples of 20 have a mean over 55? Is this close to your prediction in (d)? f) What is the probability that a single randomly chosen value (from 1 to 100) would be between 45 and 65? [Note that this is a uniform distribution, so don't use the NormalCdf command]

3. As a Group - share your data -- on the group page, list out your 4 means from the "size 5" group, and your 2 means from the "size 20" group. (due by 2/14) a) SAMPLES of size 5: List all the means from the group, including your own 60. 8 , 51. 8, 53, 42.8 45.4, 83. 2, 49.4, 46.4, 53, 39.2, 29.6, 52. 6, 69. 6, 64.2, 61.6, 45, 41.2, 42.8, 21.4, 54. 6 46. 8, 67. 8, 37.4, 27.6, 27.4, 63. 8, 75.4, 40. 2. 69. 94, 50.9, 40.98, 41.08