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:

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870