Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.72.
(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 23 specimens from the seam was 4.85. (Round your answers to two decimal places.)
(b) Compute a 98% CI for true average porosity of another seam based on 14 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.)
(c) How large a sample size is necessary if the width of the 95% interval is to be 0.42? (Round your answer up to the nearest whole number.)
(d) What sample size is necessary to estimate true average porosity to within 0.24 with 99% confidence? (Round your answer up to the nearest whole number.)