In a sample of 26 days taken at Town Talk Bakery, it was found that an average of 80 cakes perday were sold. From past surveys, the population standard deviation was found to be 34 cakes perday.a. Determine the standard error of the mean number of cakes sold per day. (Round the finalanswer to 3 decimal places.)The standard error of the mean isb. Determine the 95% confidence interval for the population mean number of cakes sold per day.(Round the z value to 2 decimal places. Round the final answers to 3 decimal places.)The 95% confidence interval for the population mean is betweenandc. Determine the 90% confidence interval for the population mean number of cakes sold per day. Ifyou wanted a wider interval, would you increase or decrease the confidence level?Increase or decrease

Suppose the prime minister wants an estimate of the proportion of the population who support his current policy on health care. The prime minister wants the estimate to be within 0.2 of the true proportion. Assume a 90% level of confidence. The prime minister's political advisors estimated the proportion supporting the current policy to be 0.47. (Round the intermediate calculation to 2 decimal places. Round the final answer to the nearest whole number.) a. How large of a sample is required? b. How large of a sample would be necessary if no estimate were available for the proportion that support current policy