An introduction to discerning the Probability of a z-Score Range is as follows. The range of z-scores in probability refers to the number of standard deviations a specific component is from the mean in a normally distributed set of data. In order to determine the probability, one must first ascertain the wanted range of z-scores. Following this, one can employ the use of a standard normal distribution table or a calculator to find the area under the curve that falls within the specified range.
| Topic | Problem | Solution |
|---|---|---|
| None | Suppose $Z$ follows the standard normal distribut… | First, we need to understand that the standard normal distribution has a mean of 0 and a standard d… |
| None | Find the area under the standard normal curve fro… | The area under the standard normal curve from 0 to a given value of $z$ is given by the cumulative … |
| None | Use the table to find the area under the standard… | The area under the standard normal curve represents the probability of an event occurring. The tota… |
| None | Assume that a set of test scores is normally dist… | Assume that a set of test scores is normally distributed with a mean of 120 and a standard deviatio… |
| None | Find the area under the standard normal curve to … | We are asked to find the area under the standard normal curve to the left of \(z=-2.03\) and to the… |
| None | Question 37 of 40 Suppose the commute times for e… | The problem is asking for the range of commute times for 95% of the employees. In a normal distribu… |
| None | Results of a survey revealed that the monthly uti… | The problem is asking for the percentage of 3-bedroom homes that had a monthly utility bill over $1… |
| None | Find the indicated probability using the standard… | The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation… |
| None | Find the area of the indicated region under the s… | The area under the standard normal curve between two points can be found by calculating the cumulat… |
| None | Find the indicated area under the standard normal… | The standard normal distribution is a special case of the normal distribution. It is the distributi… |
| None | In a survey of a group of men, the heights in the… | The problem is asking for the probability that a randomly selected participant from the study has a… |
| None | Assume the random variable $\mathrm{x}$ is normal… | Given a normally distributed random variable x with mean \(\mu = 86\) and standard deviation \(\sig… |
| None | A factory fills bottles of water. The volume of w… | Calculate the z-score for 17 ounces: \(z = \frac{17 - 16.8}{0.1} = 2\) |
| None | Question 5 of 29 Suppose a normal distribution ha… | Calculate the z-score: $$z = \frac{x - \mu}{\sigma} = \frac{47 - 50}{3} = -1$$ |
| None | When Aaron runs the 400 meter dash, his finishing… | \(\mu = 80\) |
| None | The weight of oranges growing in an orchard is no… | Find the difference between the given weight and mean weight in terms of standard deviations. |
| None | Whole Life Organic, Inc., produces high-quality o… | \(Z = \frac{X - \mu}{\sigma}\) |