A city poll will sample $n=40$ adults where the true library-card proportion is $p=0.15$. To model $\hat{p}$ with a normal distribution, what does the large counts condition say?

At a campus clinic, a random sample has $n=60$ students and the true flu-shot proportion is $p=0.80$. Before modeling $\hat{p}$ with a normal distribution, what does the large counts condition say?

An election office samples $n=250$ voters from a county where the true turnout-support proportion is $p=0.05$. For a normal model of $\hat{p}$, what does the large counts condition report?

A school surveys $n=20$ families where the true bus-use proportion is $p=0.35$. For using a normal distribution for $\hat{p}$, what is the large counts result?

A park department samples $n=80$ visitors where the true trail-map-use proportion is $p=0.90$. What does the large counts condition say before using a normal model for $\hat{p}$?

In a large population, $p=0.60$ of drivers use a hands-free phone. For samples of $n=150$, the sampling distribution of $\hat{p}$ has mean $0.60$ and standard deviation $0.04$. What z-score corresponds to $\hat{p}=0.66$, to two decimals?

Statewide, $p=0.25$ of students take the bus. For random samples of $n=300$, $\hat{p}$ has mean $0.25$ and standard deviation $0.025$. What z-score corresponds to $\hat{p}=0.20$, to two decimals?

At a plant, $p=0.42$ of bottles use recycled plastic. For samples of $n=200$, $\hat{p}$ has mean $0.42$ and standard deviation $0.035$. Standardize a sample result of $\hat{p}=0.49$ to two decimals.

In a sports league, $p=0.70$ of players wear mouthguards. For samples of $n=84$, $\hat{p}$ has mean $0.70$ and standard deviation $0.05$. What z-score is $\hat{p}=0.61$, rounded to two decimals?

At a theater, $p=0.12$ of tickets are student tickets. For samples of $n=264$, $\hat{p}$ has mean $0.12$ and standard deviation $0.02$. What is the z-score for $\hat{p}=0.15$, to two decimals?

Statewide, $p=0.25$ of students study a language other than Spanish. For $n=300$, $\hat{p}$ has mean $0.25$ and standard deviation $0.025$. Using the normal model, what is $P(\hat{p}<0.20)$ to four decimals?

In a city, $p=0.60$ of commuters use transit passes. The curve is the sampling distribution of $\hat{p}$ for $n=150$ (mean 0.60, SD 0.040). The red line marks 0.65. To four decimals, what is the probability that $\hat{p}$ is in the shaded region?

At a clinic, $p=0.25$ of appointments are no-shows. The curve is the sampling distribution of $\hat{p}$ for $n=208$ (mean 0.25, SD 0.030). The red lines mark 0.22 and 0.28. To four decimals, what is the probability that $\hat{p}$ is in the shaded region?

On a farm, $p=0.55$ of tomato plants set fruit by June. The curve is the sampling distribution of $\hat{p}$ for $n=275$ (mean 0.55, SD 0.030). The red lines mark 0.49 and 0.58. To four decimals, what is the probability that $\hat{p}$ is in the shaded region?

At a call center, $p=0.10$ of calls need a supervisor. For samples of $n=360$, $\hat{p}$ has mean $0.10$ and standard deviation $0.016$. What normal-model probability is $P(\hat{p}<0.076)$ to four decimals?

In a district, $p=0.68$ of seniors submit aid forms. For samples of $n=272$, $\hat{p}$ has mean $0.68$ and standard deviation $0.028$. To four decimals, find the normal-model probability $P(\hat{p}<0.708)$.

At a recycling center, $p=0.28$ of loads contain glass. The curve is the sampling distribution of $\hat{p}$ for $n=224$ (mean 0.28, SD 0.030). The red lines mark 0.265 and 0.325. To four decimals, what is the probability that $\hat{p}$ is in the shaded region?

For samples of $n=200$ from a population with $p=0.50$, $\hat{p}$ has mean $0.50$ and standard deviation $0.035$. One sample gives $\hat{p}=0.62$, and $P(\hat{p}\ge 0.62)\approx 0.0003$. What does that probability say?

Assume $p=0.30$ of households stream local news. For samples of $n=400$, $\hat{p}$ has mean $0.30$ and standard deviation $0.023$. A sample has $\hat{p}=0.330$, with $P(\hat{p}\ge 0.330)\approx 0.0968$. What is the judgment?

For a packaging line with true defect proportion $p=0.08$ and samples of $n=500$, $\hat{p}$ has mean $0.08$ and standard deviation $0.012$. A sample has $\hat{p}=0.11$, and $P(\hat{p}\ge 0.11)\approx 0.0062$. What does this imply?