The concept of a z-score in the field of statistics denotes the number of standard deviations a particular data point is away from the mean. Essentially, it provides a measurement of how atypical a specific value is. The process of determining the z-score involves subtracting the mean from the data point in question, then dividing the result by the standard deviation. This method proves beneficial when comparing scores across varying distributions.
| Topic | Problem | Solution |
|---|---|---|
| None | Find the value of $z_{\alpha}$. \[ \alpha=0.12 \]… | Given that \(\alpha=0.12\), we are asked to find the z-score that corresponds to the 12th percentil… |
| None | Use $z$ scores to compare the given values. The t… | Given that the tallest living man at one time had a height of 231 cm, the shortest living man at th… |
| None | Find the critical value $z_{\alpha / 2}$ that cor… | The critical value $z_{\alpha / 2}$ corresponds to the z-score that cuts off the upper $\alpha / 2$… |
| None | Find the indicated IQ score. The graph to the rig… | Given that the mean (μ) is 100, the standard deviation (σ) is 15, and the IQ score (x) is 115, we c… |
| None | Engineers want to design seats in commercial airc… | The problem is asking for the 99th percentile of the normal distribution. This is a standard proble… |
| None | A standardized exam's scores are normally distrib… | The z-score is a measure of how many standard deviations an element is from the mean. To find the z… |
| None | Find the value of $z$ such that 0.04 of the area … | This is a problem of finding the z-score in a standard normal distribution. The z-score is the numb… |
| None | Calculate the standard score of the given $X$ val… | We are given a value from the dataset, $X=40$, the mean of the dataset, $\mu=36.3$, and the standar… |
| None | Given $X=45.5, \mu=40$, and $\sigma=2$, indicate … | The problem is asking to find the position of a given value on a normal distribution curve. The nor… |
| None | A standardized exam's scores are normally distrib… | The z-score is a measure of how many standard deviations an element is from the mean. In this case,… |
| None | A standardized exam's scores are normally distrib… | The z-score is a measure of how many standard deviations an element is from the mean. To calculate … |
| None | A standardized exam's scores are normally distrib… | The z-score is a measure of how many standard deviations an element is from the mean. To find the z… |
| None | A standardized exam's scores are normally distrib… | The problem provides us with the mean test score (\(\mu\)) of 1483, the standard deviation (\(\sigm… |
| None | A standardized exam's scores are normally distrib… | Given that the mean score is 1483 and the standard deviation is 318, we need to find the z-score fo… |
| None | Assume that the age for first occurrence of filin… | Assume that the age for first occurrence of filing personal taxes follows a roughly normal distribu… |
| None | Assume that 500,000 people take the GED exam (hig… | Assume that 500,000 people take the GED exam each year and their scores form a normal distribution.… |
| None | Question 7 of 29 If a normal distribution has a m… | Given a normal distribution with mean \(\mu = 104\) and standard deviation \(\sigma = 4\), we want … |