1. Given a population where the proportion of items with a desired attribute is p = 0.25, if a sample of 400 is taken,
a. What is the standard deviation of the sampling distribution of p?
b. What is the probability the proportion of successes in the sample will be greater than 0.22?
2. Given a population in which the probability of success is p = 0.20, if a sample of 500 items is taken, then
a. Calculate the probability the proportion of successes in the sample will be between 0.18 and 0.23.
b. Calculate the probability the proportion of successes in the sample will be between 0.18 and 0.23 if the sample size is 200.
3. Given a population where the proportion of items with a desired attribute is p = 0.50, if a sample of 200 is taken,
a. Find the probability the proportion of successes in the sample will be between 0.47 and 0.51.
b. Referring to part a, what would the probability be if the sample size were 100?
4. Given a population where the probability of a success is p = 0.40, if a sample of 1,000 is taken,
a. Calculate the probability the proportion of successes in the sample will be less than 0.42.
b. What is the probability the proportion of successes in the sample will be greater than 0.44?