Assume that we need to estimate the mean of a normally-distributed population with great accuracy. Specifically, for significance level α = .01, we wish to place a confidence interval around μ such that the width of the interval is no larger than .1. Assume that the variance of the population is known to be 0.04. How large must the sample size be to assure that the width of the confidence interval is no larger than 0.1?

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?