given that $z_{20}=-2$ and $z_{50}=-1$, which of the following do you know?\nthe variance is 10.\nthe…

given that $z_{20}=-2$ and $z_{50}=-1$, which of the following do you know?\nthe variance is 10.\nthe standard deviation is 30.\nthe mean is 80.\nthe median is 40.\nthe data point $x = 20$ is 2 standard deviations from the mean.\nthe data point $x = 50$ is 1 standard deviation from the mean.\nthe data point $x = 45$ has a z - value of 1.5.\ndone

given that $z_{20}=-2$ and $z_{50}=-1$, which of the following do you know?\nthe variance is 10.\nthe standard deviation is 30.\nthe mean is 80.\nthe median is 40.\nthe data point $x = 20$ is 2 standard deviations from the mean.\nthe data point $x = 50$ is 1 standard deviation from the mean.\nthe data point $x = 45$ has a z - value of 1.5.\ndone

Answer

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $z$ is the z - score, $x$ is the data point, $\mu$ is the mean, and $\sigma$ is the standard deviation. Given $z_{20}=- 2$ and $z_{50}=-1$, we have $-2=\frac{20 - \mu}{\sigma}$ and $-1=\frac{50 - \mu}{\sigma}$.

Step2: Analyze z - score meaning

The z - score represents the number of standard deviations a data - point is from the mean. If $z_{20}=-2$, it means the data point $x = 20$ is 2 standard deviations below the mean. If $z_{50}=-1$, it means the data point $x = 50$ is 1 standard deviation below the mean. We cannot determine the variance, standard deviation, mean, or median just from the two z - scores $z_{20}=-2$ and $z_{50}=-1$. And we have no information to calculate the z - value for $x = 45$.

Answer:

The data point $x = 20$ is 2 standard deviations from the mean. The data point $x = 50$ is 1 standard deviation from the mean.