1. **Problem statement:**
Find the point estimate and 90% confidence interval for the mean price of all such college textbooks given a sample mean of 145, population standard deviation 35, and sample size 25.
2. **Point estimate:**
The point estimate of the population mean $\mu$ is the sample mean $\bar{x}$.
$$\text{Point estimate} = \bar{x} = 145$$
3. **Confidence interval formula:**
Since the population standard deviation $\sigma$ is known and the population is normal, use the z-distribution:
$$\bar{x} \pm z_{\alpha/2} \times \frac{\sigma}{\sqrt{n}}$$
where $z_{\alpha/2}$ is the critical z-value for the confidence level, $\sigma=35$, and $n=25$.
4. **Find critical z-value for 90% confidence:**
$$\alpha = 1 - 0.90 = 0.10$$
$$\alpha/2 = 0.05$$
From z-tables, $z_{0.05} = 1.645$.
5. **Calculate margin of error:**
$$ME = 1.645 \times \frac{35}{\sqrt{25}} = 1.645 \times \frac{35}{5} = 1.645 \times 7 = 11.515$$
6. **Construct confidence interval:**
$$145 \pm 11.515 = (145 - 11.515, 145 + 11.515) = (133.485, 156.515)$$
7. **Interpretation:**
We are 90% confident that the true mean price of all such college textbooks lies between 133.485 and 156.515.
**Final answers:**
- Point estimate: $145$
- 90% confidence interval: $\boxed{(133.485, 156.515)}$
Textbook Price E2B69C
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