People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior.

Question

a)What is the probability that your survey will provide a sample proportion within ±.03 of the population proportion (to 4 decimals)?


b)What is the probability that your survey will provide a sample proportion within ±.015 of the population proportion (to 4 decimals)?

Answer 1

a. µ = np = 540(.12) = 64.8
σ = √(.12*.88/540) = 0.014
z = 0.03/0.014 = 2.14
z = -0.03/0.014 = -2.14
P(-2.14 < z < 2.14) =0.9676

b. µ = np = 540(.12) = 64.8
σ = √(.12*.88/540) = 0.014
z = 0.015/0.014 = 1.07
z = -0.015/0.014 = -1.07
P(-1.07 < z < 1.07) = 0.7154

Answer 2

Thanks for your help I really appreciate it.

Answer 3

You're welcome