Question

1. stats random 3 - digit number for your mean 222 random number between 10 and 30 for standard deviation 15 fill in all blanks based on those numbers. a. b. pick a number between +2 standard deviations and +3 standard deviations and find the z - score 2.53 c. using empirical rule 68% of the population falls between 207 - 237

Explanation:

Step1: Recall the z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the data - point. Given $\mu = 222$ and $\sigma=15$.

Step2: For part b

We are given a z - score of 2.53. We can use the z - score formula to find $x$. Rearranging the formula gives $x=\mu + z\sigma$. Substituting the values, we have $x = 222+2.53\times15=222 + 37.95=259.95$.

Step3: For part c

According to the empirical rule, 68% of the data in a normal distribution lies within 1 standard deviation of the mean. So, the lower bound is $\mu-\sigma=222 - 15=207$ and the upper bound is $\mu+\sigma=222 + 15=237$.

Answer:

a. Not clear what is asked in part a.
b. If z - score is 2.53, the corresponding value $x = 259.95$
c. 207 - 237