1.A surgical technique is performed on 6 patients. You are told there is a 60% chance of success. a. Find the mean, variance, and standard deviation of the probability distribution and show the formulas used. b. Find the probability that the surgery is successful for exactly 5 patients. Show all details. Calculator strokes work for this. c. Find the probability that the surgery is successful for 2 or fewer patients. Show all details. d. What would the mean, variance and standard deviation be if the sample size was 100 patients? e. Now suppose there are 100 patients. Use the normal approximation to a binomial distribution to determine the probability of success for no more than 58 successful surgeries. 2. Find the following normal probabilities for the given parameters. a. = 3.5, = .08, P(3.36 < x < 3.64) b.=3.5, =.08, =25, (3.48<<3.52 Use the following information for exercises 3-7. In a recent year, grade 6 Michigan State public school students taking a mathematics assessment test had a mean score of 210.1 with a standard deviation of 36.6. Possible test scores could range from 0 to 400. Assume that the scores were normally distributed. 3. Find the probability that a student had a score higher than 285. 4. Find the probability that a student had a score between 180 and 305. 5. If 2000 students are randomly selected, how many will have a test score that is less than 150? 6. What is the highest score that would still place a student in the bottom 25% of the scores? 7. A random sample of 40 students is drawn from this population. What is the probability that the mean test score is greater than 250?

Perform the hypothesis tests below using the appropriate method of hypothesis testing. Make sure to show all step required for proper hypothesis testing. If you need to use a calculator (which you will) make sure to detail the steps you followed. 8a. Means - A brewery distributes beer in bottles labeled 10 ounces. Some people think they are getting less than they pay for. The local Bureau of Weights and Measures randomly selects 70 of these bottles, measures their contents and obtains a sample mean of 9.9 ounces. Assuming that is known to be 0.10 ounces, is it valid at a 0.05 significance level to conclude that the brewery is cheating the consumer? 8b. (Means) A bottling company distributes pop in bottles labeled 10 ounces. The company thinks people are getting than they paid for. The company randomly selects 35 of these bottles, measures their contents and obtains a sample mean of 10.1 ounces and a sample standard deviation of 0.20 ounces, is it valid at a 0.05 significance level to conclude that the company is giving the customer more than what they paid for?

9. (Proportion) An educator estimates that the dropout rate for seniors at high schools in Ohio is equal to 19%. Last year 12 seniors from a random sample of 200 Ohio high school seniors withdrew. At a 10% significance level, test the educator's claim. 10. Construct the 90% confidence interval for each of the following scenarios. a. You wish to estimate the proportion of automobiles that are purchased over the Internet. You took a random sample of 200 people and found that 38 purchased a car over the Internet. b. In a random sample of 17 bikers, the mean time spent riding a day was 2.813 hours and the standard deviation was 1.205. Assume the hours spent are normally distributed.

Also, know minimum sample sizes for mean and proportion.