1.A company is trying to estimate the average number of hours of overtime worked by its employees .It conducts a survey with 14 employees ,and finds the sample mean is 4.6. The variance is known to be around 4.2 . (a) Construct 390 % confidence interval for the true mean hours of overtime (b)What assumption have you made in a)? Is it likely to be true here ?What could the company do in order to avoid this assumption ? 2. A factory wishes to estimate its future use of an input to its production process ,in order to choosea suitable supplier. Data from the last 10 weeks indicates an average use of 35kg per week . The standard deviation for usage is known to be around 4kg. (3) Construct a95% confidence interval for the true mean usage . (b)The supplier that the factory would prefer to use will only be able to supply an average of 38kg a week. Would you recommend the factory use this supplier ? (c) If the supplier has a maximum supply of 36kg in any given week . how would that change your recommendation