1. For a normal population with a known variance, suppose that an investigator believe that approximately 95% values are between 38 and 70. The appropriate sample size for estimating the true population mean μ within 2 units with 95% confidence level is approximately?

2. An archer claims that 25% of her shots will be in the center of the target(i.e. a bulls-eye). A sports writer plans to test this claim by sampling 300 shots. if the 300 shots result in 60 or fewer bulls-eye(i.e. 20% bulls-eye), the writer will reject the archer's claim. what is the probability that the sports writer will reject the archer's claim, when it is actually true?