The daily caffeine intake in milligrams for adult women in a certain city is normally distributed with a mean of $180\text{ mg}$ and a standard deviation of $25\text{ mg}$. If a random sample of $36$ women is selected, what is the probability that their average daily caffeine intake is between $170\text{ mg}$ and $190\text{ mg}$?

Determine the area under the standard normal curve that lies between $z=0$ and $z=2.17$.

Let the variable $Z$ have a uniform distribution from $1$ to $13$. What is the probability that $Z$ is between $3$ and $9$?

Find the probability that a male has a height between $160\text{ cm}$ and $190\text{ cm}$, given that the distribution of heights for males is normal with a mean of $175\text{ cm}$ and a standard deviation of $6\text{ cm}$.

The table below shows the population statistics for the ages of Olympic gold medalists in the $100$-meter sprint and the marathon from $1950$ to $2020$. The distributions are approximately normal.

In $2016$, the $100$-meter sprint gold medalist was $34$ years old, and the marathon gold medalist was $28$ years old. Who had a more unusual age for their event?

The time it takes for a commuter to drive to work is normally distributed with a mean of $40$ minutes and a standard deviation of $7$ minutes. What is the probability that a randomly selected commute takes between $40$ and $54$ minutes?

Which of the following best captures the defining difference between a discrete random variable and a continuous random variable?

Derive the height of the pdf for a uniform distribution on [A,B] by equating the total area under a constant pdf to 1.

Let X ~ Uniform[0, 12]. You are asked: given that X > 8, compute P(X ≤ 11 | X > 8).

Determine the $z$-score for which the area to the right is $0.025$.

In a binomial experiment with $n$ trials and a success probability of $p$, when can the distribution of $X$ be approximated by a normal distribution, and what are its mean and standard deviation?

A shipment contains $n=50$ items and each item has probability $p=0.12$ of being defective, independently. Using a normal approximation with continuity correction, approximate the probability that exactly $7$ items are defective.