In the context of a $99\%$ confidence interval, what does the $99\%$ refer to?

A factory produces light bulbs with a mean lifetime of $1200$ hours and a standard deviation of $100$ hours. If a quality control manager selects a random sample of $25$ bulbs, what is the probability that the sample mean lifetime is greater than $1230$ hours?

The time (in minutes) it takes to assemble a product is left-skewed with a mean of $20$ and a standard deviation of $6$. If random samples of size $36$ are selected, what is the shape of the sampling distribution of the sample mean?

A quality control expert is performing a hypothesis test on the mean weight of a product and needs to find the critical value for a $98\%$ confidence interval based on a sample of $15$ items. If the degrees of freedom are $\text{df}=14$, what value of $\alpha$ should be used to look up the $t$-critical value, $\pm t_{\alpha /2}$, in a standard $t$-distribution table?

A bell-shaped sampling distribution of the sample mean $\bar{x}$ is shown below. The center is at $640$, and the dashed vertical lines appear at $620$ and $660$. What is the value of ${\mu }_{\bar{x}}$?

A clinic's long-term average appointment duration is $50$ minutes. After a scheduling change, a sample of $n=10$ appointment lengths (in units of minutes) is recorded: $45,51,47,49,50,52,46,48,53,44$. To perform a null bootstrap under $\mu =50$, what is the null-centered sample $\left\{x_i^{\left(0\right)}\right\}$?

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 university claims that the average weight of textbooks for its engineering students is $7.5$ pounds. A random sample of $36$ engineering students' textbook weights is taken, yielding a sample mean of $6.8$ pounds. If the population standard deviation is known to be $1.8$ pounds, what is the probability of obtaining a sample mean of $6.8$ pounds or less?

A bell-shaped sampling distribution of the sample mean $\bar{x}$ is shown below. The center is at $640$, and the dashed vertical lines appear at $620$ and $660$. What is the value of ${\sigma }_{\bar{x}}$ (the standard error of $\bar{x}$)?

The mean daily rainfall in a rainforest region is normally distributed with a mean of $18.2\text{ mm}$ and a standard deviation of $6.3\text{ mm}$. If a sample of $10$ days is randomly chosen, what is the probability that the sample mean rainfall is between $14.4$ and $21.7\text{ mm}$?