A philanthropic organisation sent free mailing labels and greeting cards to a random sample of 100 comma 000100,000 potential donors on their mailing list and received 47034703 donations. (a) Give a 9999% 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 4.74.7%. Given the confidence interval you found, do you find that rate plausible?