During the course of a typical baseball​ season, suppose that a batter has 500​ at-bats. This means that the player has the opportunity to get a hit 500 times during the course of a season.​ Further, suppose that a batter is a career 0.280 hitter​ (he averages 280 hits for every 1000​ at-bats, or he has 280 successes in 1000 trials of the​ experiment), so the population proportion of hits is 0.280. ​(a) Assuming that each​ at-bat is an independent​ event, describe the sampling distribution of p​, the proportion of hits in 500​ at-bats over the course of a season. ​(b) Would it be unusual for a player who is a career 0.280 hitter to have a season in which he hits​ 0.310? ​(c) Would it be unusual for the player who hit 0.310 one season to hit below 0.255 the following​ season? ​(a) The sampling distribution of p is ▼

An air conditioning system can circulate 350 cubic feet of air per minute. how many cubic yards of air can it circulate per minute?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

Arandomized controlled trial is designed to evaluate the effect of metoprolol in patients with heart failure. while preparing for statistical analysis, the researcher reviews some common types of statistical errors. which of the following statements is true regarding a type i error in a clinical study? a. the study is not significantly powered to detect a true difference between study groups. bthe null hypothesis is true but is rejected in error. c. the null hypothesis is false but is accepted in error. d. type i error is also known as beta and is usually 0.1 or 0.2. e. type i error depends on the study's confidence interval.