Math 1401 Chapters 15 & 16 Classwork Name_Raven porter Sampling Distributions/Confidence Intervals Time of Class Meeting M . W F 9-9:50 Use this information to answer questions 1 - 6) In a famous research paper in the psychology literature, George Miller found that the amount of information humans can process in short-term memory was 7 bits (pieces of information), plus or minus 2 bits. Assume that the number of bits retained in short-term memory is normally distributed with a mean of 7 and the standard deviation is 2. Suppose that we take a simple random sample of 36 people and test their short-term memory skills. 1. Find the probability that the sample mean number of bits retained in short-term memory is greater than 7.5. 0.0648 2. Find the probability that the sample mean number of bits retained in short-term memory is between 6.8 and 7.2. 0.40 0. LO 0. 7257 0. 7257 0 . 45 15 3. Find the probability that the sample mean number of bits retained in short-term memory is less than 6.75. 0 . 22 60 60 4. Find the 97.5th percentile of the sample mean number of bits retained in short-term memory. 5. Find the 2.5th percentile of the sample mean number of bits retained in short-term memory. lie? Between what two values do the middle 95% of the sample mean number of bits retained in short term memor 7. (Checking the conditions.) For each of the following situations, simple random samples are drawn. Indicate whether or not we can use a Z-Interval. Answer "Yes" or "No". a. The sample size is large ( n 2 30) and o is unknown. b. The original population is normal, sample size is 9, and o is known. c. The sample size is large ( n 2 30) and o is known. d. The sample size is small, the original population is heavily skewed to the right, and o is known. The sample size is large ( n 2 30), the original population is not normal, and o is known The original population is not normal, and o is unknown