#1 : In grading eggs into small, medium, and large, the Lahore Farms packs the eggs that weigh more than 3.6 ounces in packages marked "large" and the eggs that weigh less than 2.4 ounces into packages marked "small"; the remainder are packed in packages marked "medium." If a day's packaging contained 10.2% large and 4.18% small eggs, determine the mean and the standard deviation for the eggs' weights. Assume that the distribution of the weights is normal. Q2 # Initial salaries of a sample of 5 administrators along with their genders are shown below. Employee Salary ($1000s) Gender 1 30 F 2 28 M 3 22 F 4 26 F 5 19 M a. What is the point estimate for the initial salaries of all administrators? b. Determine the point estimate for the variance of the population. c. Determine the point estimate for the proportion of male employees. Q4#. QAU university planner wants to determine the proportion of spring semester students who will attend summer school. She surveys 32 current students discovering that 12 will return for summer school. a. Construct a 90% confidence interval estimate for the proportion of current spring students who will return for summer school. b. With a 0.95 probability, how large of a sample would have to be taken to provide a margin of error of 3% or less? Q5#. Hand Logo company is considering a promotion that will offer customers to purchase a toy featuring a cartoon movie character. If more than 20% of the customers purchase the toy, the promotion will be profitable. A sample of 50 restaurants is used to test the promotion. a. State the hypotheses associated with the restaurant's test. b. Describe a Type I error for this situation. c. Describe a Type II error for this situation. Q6#. A furniture company advertises that it will deliver your furniture within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be 5.6 days. a. State the null and alternative hypotheses. b. Using a critical value, test the null hypothesis at the 5% level of significance. c. Using a p-value, test the hypothesis at the 5% level of significance. d. What type of error may have been committed for this hypothesis test? Q7#. Marks on a CSS exam were normally distributed with a mean of 60 and a variance of 36. a. Find the probability that a randomly selected CSS exam will have a mark of at least 66? b. What percentage of CSS exams will have marks between 48 and 51? c. If the top 3.92% of CSS marks receive merit awards, what is the lowest mark eligible for an award? d. If there were 334 CSS exams with marks of at least 69, how many students took the exam