Question 7.106

106. Short-Term Memory. In a famous research paper in the psychology literature, George Miller found that the amount of information humans could process in short-term memory was 7 bits (pieces of information), plus or minus 2 bits.5 Assume that the mean number of bits is 7 and the standard deviation is 2, and that the distribution is normal. Suppose we take a sample of 100 people and test their short-term memory skills.

  1. Find the probability that the sample mean number of bits retained in short-term memory lies between 6.8 and 7.2.
  2. Between which two values do the middle 95% of sample mean number of bits retained in short-term memory lie?