1: A sample of 8 people receive an average hourly pay of 9.50 with a standard deviation of 50p. Calculate a 95% confidence interval for the mean hourly rate of pay, assuming that the rates of pay are normally distributed. How would your answer change if you were unsure about the probability distribution of your sample? Problem 2: Suppose that Ho: M = 100, Hy: M 100, at a significance level of 5%. If a test result is 2.07 standard deviations from the mean would you reject or not reject the Null hypothesis? Problem 3: The A launderette operates a large washing machine. When working properly the duration of each wash is normally distributed with a mean of 50 minutes. The manager tests the machine by carrying out 5 washes and obtains a sample average of 55 minutes with a standard deviation of 5 minutes. What is the probability of this result when the null hypothesis is true? Problem 4: Nori rolls a pair of standard, six-sided dice. What is the probability that the sum of the two dice is 6? Problem 5: 35 fifth graders have a mean reading score of 82. The standard deviation of the population is 15. Find the 95% confidence interval estimate for the mean reading scores of all fifth graders. Problem 6: A binomial distribution has a probability of success of 0.5. What is the probability of 5 successes in 10 trials