Q5. Please show working in full and please hand write solutions clearly (please don't type)

Q5(8). A random sample with sample size of 25 was selected from a normal population. The population variance is unknown. The 95% two sided confidence interval is calculated as (6, 8). 1(4). Apply the same sample to calculate the 99% confidence interval. 2(4). If we would like a narrower confidence interval. Use the sample information described in question above as previous experience, that is, assuming the same sample variance. Calculate the minimum sample size such that the 95% confidence interval width is 1