What influences the sample size? we examine the effect of different inputs on determining the sample size needed to obtain a specific margin of error when finding a confidence interval for a proportion. find the sample size needed to give, with 95% confidence, a margin of error within plus-or-minus 6% when estimating a proportion. first, find the sample size needed if we have no prior knowledge about the population proportion p. then find the sample size needed if we have reason to believe that p almost-equals 0.7. finally, find the sample size needed if we assume p almost-equals 0.8.

Aschool typically sells 500 yearbooks each year for 50 dollars each. the economic calls does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price. the revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook. let x represent the number of $5 decrease in price. if the expression that represents the revenue is written in the form r(x)=(500+ax)(50-bx). to maximize profit, what price should the school charge for the yearbooks? what is the possible maximum revenue? if the school attains the maximum revenue, how many yearbooks will they sell?

The krasnapolski is a top-of-the-line hotel in amsterdam, the netherlands. among their many services, they rent bicycles to guests. the bicycle checkout is open 24 hours per day 7 days per week and has 50 bicycles on hand. on average, 10 guests request a bicycle each day, arriving completely randomly at all times of the day during the spring and summer seasons. guests keep bicycles for four days on average, with a standard deviation of two days. how long does a guest on average have to wait for a bike? a. approximately 24 hours b. approximately 0.033 hours c. approximately 4 days d. approximately 47 minutes

The multiplicative property of equality states that for real numbers a, b, c, and d, if a = b and c = d, then ac = bd. true false