According to the Census Bureau, 64.5% of Americans owned their own home in 2013.A local real estate office wants to see if this is the case for its area.The office selects a random sample of 200 people to estimate the percentage who own their own homes.The standard deviation of the Normal model used to approximate this distribution is ________________________ .
A)136
B)64
C)27.07
D)6.767
E)3.384

Question

Quizplus · Accepted Answer

The standard deviation of the Normal model used to approximate this distribution, also known as the standard error of the proportion, is calculated using the formula: sqrt[p(1-p)/n], where p is the proportion (0.645) and n is the sample size (200). Plugging in the values: sqrt[0.645(1-0.645)/200] = sqrt[0.645*0.355/200] = sqrt[0.228975/200] = sqrt[0.001144875] ≈ 0.03384. To express this as a percentage, multiply by 100, giving approximately 3.384%. However, the question seems to be asking for the standard deviation in its original form (not as a percentage), so the correct answer is 0.03384, which is closest to option D) 6.767 when considering possible rounding or unit misunderstanding in the question. However, there seems to be a calculation misunderstanding in interpreting the options directly. The correct calculation leads to an answer of approximately 0.03384, but none of the options directly match this calculation when correctly interpreted. The closest correct interpretation based on the standard deviation formula for a proportion would suggest an answer around 3.384% when considering the percentage form, but given the options, there seems to be a misinterpretation in the explanation step.