Find the $z$-score that corresponds to the following percentile:

$\text{P}2.5$

In a survey of weekly hours spent on online courses by a group of students, the following hours were reported: $5$, $8$, $10$, $12$, $15$, $7$, $9$, $11$, $6$, $8$, $10$, and $7$. Calculate the $z$-score for the student who spent the most hours online.

Determine the probability that a standard normal variable $Z$ is less than $-0.52$.

The heights of adult male giraffes in a wildlife reserve are bell-shaped with a mean of $17.2$ feet and a standard deviation of $1.1$ feet. A particular giraffe is measured at $14.7$ feet. Calculate the $z$-score for this giraffe's height and determine if it is unusual.

The figure below shows the continuous uniform distribution of customer waiting times at a coffee shop. Determine the mean and standard deviation for the distribution of the waiting times.

If a problem asks for the probability that z is less than a certain value, which tail is being referenced?

A TI-84 Plus (not CE) only accepts left-tail areas. You are given P(z > b) = 0.30. What area should you input to find z?

The distribution of ages for marathon winners in a certain city is approximately bell-shaped, with a mean of $32.5$ years and a standard deviation of $4.2$ years. In $2012$, the winner was $43$ years old. Find the $z$-score for this age and state whether it is unusual.

What are the mean and standard deviation of the standard normal distribution?

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