A continuous random variable $𝑋$ is uniformly distributed between $10$ and $30$ minutes. Draw the graph of the uniform density function for $𝑋$.

A normally distributed variable $N$ has a mean of $100$ and a standard deviation of $10$. Find .

A cumulative probability of 0.5000 corresponds to which z score?

Assume that the marks on a test are normally distributed with a mean of $0$ and a standard deviation of $1$. Draw a graph of the standard normal curve and answer the following question. If a student is randomly selected and given this test, what is the probability that their score is greater than $1.82$?

In a recent study, $48\%$ of employees reported that they would consider working remotely full-time. If a company randomly selects $350$ employees, what is the probability that at least $180$ would consider working remotely full-time? Use the normal approximation if appropriate, and state whether this is an unusual event.

In a study, hemoglobin levels in adult males are normally distributed with a mean of $15.5$ grams per deciliter and a standard deviation of $1.1$ grams per deciliter. What percentage of adult males have a hemoglobin level less than $17$ grams per deciliter?

The graph depicts the standard normal distribution of test scores with a mean of $0$ and a standard deviation of $1$. Find the indicated z-score.

What might happen if you do not set appropriate window parameters before using the shadeNorm function?

In a survey of $180$ employees, the highest monthly salary recorded was $\mathrm{\backslash (}7,200$. The mean monthly salary was $\mathrm{\backslash )}5,400$ with a standard deviation of $\$600$. What is the $z$-score for the highest salary? Express your answer with two decimal places.

Suppose exam scores in a statistics course are normally distributed with a mean of $72.4$ and a standard deviation of $8.5$. What is the probability that a randomly selected student scored higher than $86$? Is this considered an unusual event?

The weights of packages shipped by a company are normally distributed with a mean of $12$ pounds and a standard deviation of $2$ pounds. What is the probability that a randomly selected package weighs more than $16$ pounds?

In a group of $250$ dolphins, the average body length is $2.7$ meters with a standard deviation of $0.3$ meters. The data are normally distributed. Calculate the $z$-score for a body length of $3.4$ meters and determine if this is unusual.

Select the choice that correctly describes three meanings of the area under a normal density curve to the left of a point $x_0$.

A normal distribution has a mean of $\mu =15$ and a standard deviation of $\sigma =4$. What is the probability that $X$ falls between $18$ and $23$?

A poll claims that $4\%$ of adults prefer electric scooters. You sample $400$ commuters and find $25$ who prefer electric scooters. Compute the probability that, in a random sample of $400$ commuters, at least $25$ prefer electric scooters assuming the true proportion is $4\%$.