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## STAT 135 LAB 11

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**STAT 135 LAB 11**Learning Objective: #72 TA: Dongmei Li**Simulations in the Law of Average Lab (Lab 10)**The number of red marbles in 38 trials: 16 16 19 17 26 13 with standard deviation =4.44597 Corresponding proportions (number of red marbles in 38 trials/38): 0.421053 0.421053 0.500000 0.447368 0.684211 0.342105 with standard deviation = 0.116999 The number of red marbles in 3800 trials: 1786 1792 1777 1826 1758 1822 with standard deviation=26.304 Corresponding proportions (number of red marbles in 3800 trials/3800): 0.470000 0.471579 0.467632 0.480526 0.462632 0.479474 with standard deviation = 0.00692210 • Conclusions: • When there are more trials, the proportions are likely to be more stable. • When there are more trials, the counts are likely to be more variable.**A Question**Which is more likely to follow a normal distribution? • The weights of a randomly selected cartoon of large eggs from the grocer store shelf • The heights of all of the students in stat 135**Sampling distribution**Take many samples (of same size) from the same population and calculate the sample mean or sample proportion from each sample. We can look at a distribution of the sample means or sample proportions. Sample mean and sample proportion are approximately normal if some conditions (see next slide) are satisfied.**Best normal approximation**• When sample size is large ( ) • If and • If is close to and sample size is large**Learning Objective**72. The quality of the normal approximation improves with larger sample sizes and symmetry of the parent population.