The proportion of homes in Washington owned by investors rather than homeowners is $22 \%$. In order to determine if the of homes owned by investors has changed, researchers take a sample of 300 recently purchased homes and find that 76 ar owned by investors.
Complete the formula and calculation of the standard deviation.
\[
\text { standard deviation }=\sqrt{\frac{a \cdot b}{300}}
\]
\[
a=
\]
\[
b=
\]
Your answer should be in decimal format.
Submit
Answer
\(\boxed{\text{So, the standard deviation is approximately 0.0239.}}\)
Step 1 ：\(a = 0.22\)
Step 2 ：\(b = 1 - a = 1 - 0.22 = 0.78\)
Step 3 ：Substitute 'a' and 'b' into the formula for standard deviation: \(\text{standard deviation} = \sqrt{\frac{a \cdot b}{300}} = \sqrt{\frac{0.22 \cdot 0.78}{300}}\)
Step 4 ：Calculate the expression under the square root: \(0.22 \times 0.78 = 0.1716\)
Step 5 ：\(0.1716 / 300 = 0.000572\)
Step 6 ：The standard deviation is the square root of 0.000572: \(\sqrt{0.000572} \approx 0.0239\)
Step 7 ：\(\boxed{\text{So, the standard deviation is approximately 0.0239.}}\)
