Assume we have a batch of 1000 batteries including 950 that are good and 50 that are defective. Assume 100 of those 1000 batteries are selected without replacement. Your goal is to find the Number of successes in the sample. Show work please!

You are a medical researcher that wants to determine if your new drug can lower people's blood pressure.  You recruit 60 participants with high blood pressure to be part of your study.  You randomly assign participants to one of three groups to receive either 10 mg of your drug, 5 mg, or 0 mg (given as a placebo control).  After 2 weeks, participants' blood pressure is measured and you compare among the 3 groups. Which statistical test would be best to determine if there is a significant difference in blood pressure among the three groups?

A lawn mower company will produce 1,500 lawn mowers by 2020. In an effort to determine how much maintenance-free consumers will buy when they buy lawn mowers, the company decided to conduct a study over the past 1 year of these mowers. First, a random sample was taken by contacting 200 grass mowers. The company owner provides an 800 number and is asked to contact the company when the first repair is needed for the lawn mower. Owners who no longer use lawn mowers to cut their grass are either disqualified or not sampled. After 1 year, it turned out that 187 owners had reported for the first repair. However, the other 74 disqualified themselves. The average number per year until the first improvement was 5.3 times for samples deemed feasible. It is believed that the standard deviation is 1.28 per year. If the company wants to advertise the lawnmower and with a confidence level of 95%, what is the estimated annual mean value of repair-free lawn mower for this lawn mower? What is the…

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A personal trainer wanted to test the effectiveness of two different workout routines. She took a random sample of 70 of her clients and, in a random order, had them complete one of the two routines for two weeks. Then, after a one-month waiting period, she asked them to come back and do the other routine for two weeks. After each two-week period of the exercise routines, she measured their performance on a physical fitness aptitude test. She found the average difference in aptitude scores between the two routines for each client was 30.4 with a standard error of 3.2. What would be her 85% confidence interval for the average difference in the effectiveness of the two routines? (3 decimal places) (  ,  )