Answer:
C) 5.1%
Step-by-step explanation:
To find the standard deviation of the sampling distribution of the proportion for small autos, we can use the formula for the standard deviation of the sampling distribution of sample proportions:
[tex]\sigma_{\hat{p}} = \sqrt{\dfrac{p(1-p)}{n}}[/tex]
where:
- p is the population proportion.
- n is the sample size.
From the given pie chart, the population proportion for small autos is 37%, so p = 0.37:
[tex]\sigma_{\hat{p}} = \sqrt{\dfrac{0.37(1-0.37)}{n}}\\\\\\\\\sigma_{\hat{p}} = \sqrt{\dfrac{0.2331}{n}}[/tex]
The random sample is 90 automobiles, so substitute n = 90 into the formula:
[tex]\sigma_{\hat{p}} = \sqrt{\dfrac{0.2331}{90}}\\\\\\\\\sigma_{\hat{p}} = 0.05089204...\\\\\\\sigma_{\hat{p}} \approx 5.1\%[/tex]
Therefore, the approximate standard deviation of the sampling distribution of the proportion for small autos is:
[tex]\LARGE\boxed{\boxed{5.1\%}}[/tex]
