A botanist is studying the height of a rare plant species. Out of a population of $150$ plants, the mean height is $32.4\text{ cm}$ with a standard deviation of $8.1\text{ cm}$. If a random sample of $40$ plants is chosen, what is the probability that the sample mean height is between $30\text{ cm}$ and $35\text{ cm}$? Should the finite correction factor be used?

A company’s filling machine dispenses essential oil with a mean of $11.96$ ml and a standard deviation of $0.05$ ml. A quality inspector randomly selects three separate samples, each containing five bottles, and measures the sample mean fill amount for each. What is the probability that at least one of these three samples has a sample mean within the acceptable range of $11.90$ ml to $12.00$ ml?

A random sample of patient weights (in pounds) is $\{150,160,155,170,165\}$. Which of the following could be a valid bootstrap sample drawn from this sample (sampling with replacement)?

The distribution of the time to complete a vehicle safety inspection is skewed to the right. Records show the mean inspection time is $9.8$ minutes with a standard deviation of $4.1$ minutes. What sample size is commonly required so that the sampling distribution of the sample mean can be approximated by a normal distribution for probability calculations?

True or False: If you want to decrease the standard error of the mean by a factor of $5$, you must increase the sample size by a factor of $25$.