A philanthropic organisation sent free mailing labels and greeting cards to a random sample of 100,000 potential donors on their mailing list and received 4845 donations.

(a) Give a 90% confidence interval for the true proportion of those from their entire mailing list who may donate.

(b) A staff member thinks that the true rate is 4.5%. Given the confidence interval youfound, do you find that rateplausible?