An orchard researcher takes every possible random sample of 25 apples, records the average mass in grams for each sample, and graphs all those averages. What distribution is this?

A school repeats every possible random sample of 80 students and records the proportion who ate breakfast that day. In the resulting sampling distribution, what does each plotted value represent?

A bottling plant has a fixed population mean fill of $\mu =501$ mL. If many random samples of 10 bottles are taken, what varies from sample to sample?

Every possible random sample of 40 clinic patients is taken, and the proportion who waited over 10 minutes is computed for each sample. The collection of those proportions is called what?

Household water use in a city is strongly right-skewed with $\mu =140$ liters and $\sigma =90$ liters per day. For random samples of 100 households, what does the central limit theorem say about $\bar{x}$?

Call-center wait times have $\mu =6.0$ minutes and $\sigma =4.5$ minutes and are not normal. Which random sample size is large enough for the central limit theorem to justify a normal model for $\bar{x}$?

At a factory, $p=0.08$ of parts are defective. For random samples of 40 parts, is a normal model for $\hat{p}$ justified by the large-counts condition?

Tree diameters in a forest are skewed with $\mu =32$ cm and $\sigma =14$ cm. As random sample size grows from 25 to 100, what central-limit effect should occur for $\bar{x}$?

Adult heights in a population have $\mu =170$ cm and $\sigma =8$ cm. For random samples of 64 adults, what are the mean and standard deviation of $\bar{x}$?

Chocolate bars have approximately normal masses with $\mu =52$ g and $\sigma =4$ g. For random samples of 16 bars, what is the shape, mean, and standard deviation of $\bar{x}$?

Commute times for city workers are right-skewed with $\mu =28$ minutes and $\sigma =12$ minutes. For random samples of 36 workers, what describes the sampling distribution of $\bar{x}$?

A filling machine has bottle amounts with $\mu =750$ mL and $\sigma =15$ mL. For random samples of 25 bottles, what is the standard deviation of the sampling distribution of $\bar{x}$?

A salmon hatchery has fish masses with $\mu =75$ g and $\sigma =10$ g. When random sample size changes from 25 fish to 100 fish, what happens to the center and spread of $\bar{x}$?

In a large town, $p=0.40$ of commuters bike to work. For random samples of 150 commuters, what are the mean and standard deviation of $\hat{p}$, rounded to three decimals?

In a county, $p=0.62$ of voters support a park bond. For random samples of 200 voters, use normal approximation; area below $z=1.75$ is 0.960. To three decimals, what is $P(\hat{p}>0.68)$?

At a machine, $p=0.12$ of bolts are defective. For random samples of 100 bolts, what is the shape and center of the sampling distribution of $\hat{p}$?

A clinic knows $p=0.25$ of appointments are no-shows. For random samples of 64 appointments, what is the standard deviation of $\hat{p}$, rounded to three decimals?

Bags leaving a plant have $\mu =50.0$ kg and $\sigma =1.2$ kg. For random samples of 16 bags, area below $z=2$ is 0.977. To three decimals, what is $P(\bar{x}>50.6)$?

Juice bottles are measured in mL. For random samples of 25 bottles, area below $z=2$ is 0.9772 and below $z=-2$ is 0.0228. To three decimals, what is the probability represented by the shaded interval for $\bar{x}$?

Light-bulb lifetimes have $\mu =800$ hours and $\sigma =48$ hours. For random samples of 36 bulbs, area below $z=-1.5$ is 0.067. To three decimals, what is $P(\bar{x}<788)$?