1. Strategic business planning is required for the successful transfer of control between generations in family-owned companies. However, a survey of 262 privately held family firms whose annual turnover exceeded one million dollars it was found that 116 had no strategic business plan. Assuming that simple random sampling was employed to determine the sample for the survey, estimate with 85% confidence the proportion of family-owned companies operating without strategic business plans. Give the lower limit only and report your answer correct to three decimal places.
2. The time taken to service a particular type of machine is known to be approximately normally distributed. A random sample of 76 past services revealed a mean time taken of33 hours and a variance of 38.12 hours squared. Calculate the 90% confidence interval for the mean. State the lower bound only of this confidence interval correct to three decimal places.