Let's go through each part of the question.

Part (a)

The best point estimate for the population mean temperature is the sample mean. Given in the problem, the mean of the measurements is 63 degrees Fahrenheit. So, the answer for (a) is:

• 63 degrees

Part (b)

We need to choose the appropriate distribution (Z, t, or other) for each scenario to calculate the 99% confidence interval.

1. Sample size 90 from a non-normally distributed population:

   • Since the sample size is large (greater than 30), the Central Limit Theorem applies, allowing us to use the Z-distribution.
   • Answer: Z

2. Sample size 12 from a normally distributed population with an unknown standard deviation:

   • With a small sample size and unknown standard deviation, we use the t-distribution.
   • Answer: t

3. Sample size 17 from a normally distributed population with a known standard deviation of 3.3:

   • Since the population is normally distributed and the standard deviation is known, we can use the Z-distribution even with a smaller sample size.
   • Answer: Z

Would you like further details on these answers, or do you have any questions?

Related Questions

1. What is the significance of the Central Limit Theorem in confidence intervals?
2. How does the t-distribution differ from the Z-distribution in confidence interval estimation?
3. When is it appropriate to use a confidence interval with a small sample size?
4. Why is knowing the population standard deviation important in selecting the correct distribution?
5. How does sample size affect the choice of distribution for confidence intervals?

Tip: Always check if the population standard deviation is known when determining whether to use the Z or t distribution.