To find the 95% confidence interval estimate of the mean mileage, we can use the formula for the confidence interval of the mean when the sample size is large (n 30). The formula is:

$$ \text{CI} = \bar{x} \pm z \left( \frac{\sigma}{\sqrt{n}} \right) $$

where:
- $\bar{x}$ is the sample mean
- $z$ is the z-value corresponding to the desired confidence level
- $\sigma$ is the sample standard deviation
- $n$ is the sample size

Given:
- $\bar{x} = 28.5$
- $\sigma = 1.2$
- $n = 30$
- For a 95% confidence level, the z-value is approximately 1.96

Step-by-step calculation:

1. Calculate the standard error (SE):
$$ \text{SE} = \frac{\sigma}{\sqrt{n}} = \frac{1.2}{\sqrt{30}} \approx \frac{1.2}{5.477} \approx 0.219 $$

2. Calculate the margin of error (ME):
$$ \text{ME} = z \times \text{SE} = 1.96 \times 0.219 \approx 0.429 $$

3. Calculate the confidence interval:
$$ \text{CI} = \bar{x} \pm \text{ME} $$
$$ \text{CI} = 28.5 \pm 0.429 $$

So, the lower limit of the confidence interval is:
$$ 28.5 - 0.429 = 28.071 $$

And the upper limit of the confidence interval is:
$$ 28.5 + 0.429 = 28.929 $$

Therefore, the 95% confidence interval estimate of the mean mileage is approximately (28.1, 28.9).

The correct answer is:
(28.1, 28.9)

Question

To find the 95% confidence interval estimate of the mean mileage, we can use the formula for the confidence interval of the mean when the sample size is large (n > 30). The formula is:

$$ \text{CI} = \bar{x} \pm z \left( \frac{\sigma}{\sqrt{n}} \right) $$

where:
- $\bar{x}$ is the sample mean
- $z$ is the z-value corresponding to the desired confidence level
- $\sigma$ is the sample standard deviation
- $n$ is the sample size

Given:
- $\bar{x} = 28.5$
- $\sigma = 1.2$
- $n = 30$
- For a 95% confidence level, the z-value is approximately 1.96

Step-by-step calculation:

1. Calculate the standard error (SE):
$$ \text{SE} = \frac{\sigma}{\sqrt{n}} = \frac{1.2}{\sqrt{30}} \approx \frac{1.2}{5.477} \approx 0.219 $$

2. Calculate the margin of error (ME):
$$ \text{ME} = z \times \text{SE} = 1.96 \times 0.219 \approx 0.429 $$

3. Calculate the confidence interval:
$$ \text{CI} = \bar{x} \pm \text{ME} $$
$$ \text{CI} = 28.5 \pm 0.429 $$

So, the lower limit of the confidence interval is:
$$ 28.5 - 0.429 = 28.071 $$

And the upper limit of the confidence interval is:
$$ 28.5 + 0.429 = 28.929 $$

Therefore, the 95% confidence interval estimate of the mean mileage is approximately (28.1, 28.9).

The correct answer is:
(28.1, 28.9)

Knowee AI · Accepted Answer