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?

a) 99% Confidence interval:  (0.045311,0.04875)

b) 4.7% is a plausible rate.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 100,000

Number of people who donated, x = 4703

a) 99% Confidence interval:

Putting the values, we get:

b) A staff member thinks that the true rate is 4.74.7%.

Yes, this is a plausible rate as this value of 0.0474 lies in the calculated confidence interval as:

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