The dashed lines represent the mean and $1$-standard-deviation intervals in the following normal distribution. Estimate the values of the mean and standard deviation.

A company designs workstations for employees whose seated elbow heights are normally distributed with a mean of $27.8$ inches and a standard deviation of $1.6$ inches. If a workstation is uncomfortable for those with elbow heights less than $24.2$ inches, what percentage of employees will find the workstation uncomfortable?

In a certain city, the IQ scores of adults are normally distributed with a mean of $100$ and a standard deviation of $15$. A local university offers a scholarship to individuals whose IQ is in the top $2.5\%$. What is the minimum IQ score required to qualify for this scholarship?

The scores on a college entrance exam are normally distributed with a mean of $600$ and a standard deviation of $90$. What is the probability that a randomly selected student scores above $720$?

Suppose the random variable $z$ is normally distributed with a mean $\mu =15.7$ and a standard deviation $\sigma =5.2$. Find .

Find the area under the standard normal curve between $z=0$ and $z=1.60$.

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 $190\text{ mg}$?

If the area to the right of a z score is 0.10, what is the z score?

In a study of foot lengths, it was found that the lengths are normally distributed with a mean of $250\text{ mm}$ and a standard deviation of $15\text{ mm}$. A shoe company decides to design shoes that will not fit individuals whose foot lengths fall in the smallest $2.5\%$ or the largest $2.5\%$ of the population. What is the range of foot lengths that the shoes will cover?

Find the probability that the standard normal variable $Z$ is less than $1.57$.