Question

each person in a group of friends counted the number of books they read in one year. the mean number of books read was 34, with a standard deviation of 3.5. the number of books read by four of the friends is shown below. match each student with their z - score, rounded to the nearest hundredth. annabelle read 21 books. bianca read 17 books. catherine read 42 books. delaney read 34 books. anabelle z = bianca z = catherine z = delaney z =

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the individual value, $\mu$ is the mean, and $\sigma$ is the standard deviation. Here, $\mu = 34$ and $\sigma=3.5$.

Step2: Calculate Annabelle's z - score

For Annabelle, $x = 21$. Substitute into the formula: $z_{Annabelle}=\frac{21 - 34}{3.5}=\frac{- 13}{3.5}\approx - 3.71$.

Step3: Calculate Bianca's z - score

For Bianca, $x = 17$. Substitute into the formula: $z_{Bianca}=\frac{17-34}{3.5}=\frac{-17}{3.5}\approx - 4.86$.

Step4: Calculate Catherine's z - score

For Catherine, $x = 42$. Substitute into the formula: $z_{Catherine}=\frac{42 - 34}{3.5}=\frac{8}{3.5}\approx2.29$.

Step5: Calculate Delaney's z - score

For Delaney, $x = 34$. Substitute into the formula: $z_{Delaney}=\frac{34 - 34}{3.5}=0$.

Answer:

Annabelle: - 3.71
Bianca: - 4.86
Catherine: 2.29
Delaney: 0