the first stats exam had a mean of 65 and a standard deviation of 10 points; the second had a mean of 75 and…

the first stats exam had a mean of 65 and a standard deviation of 10 points; the second had a mean of 75 and a standard deviation of 5 points. derrick scored a 75 on both tests. julie scored a 70 on the first test and an 80 on the second. they both totaled 150 points on the two exams, but julie claims that her total is better. explain. select the correct choice below and, if necessary, fill in the answer boxes within your choice. (round to three decimal places as needed.) a. julies claim is incorrect. derricks z - scores are for the first test and for the second test. derricks total is, which is more than julies total. b. julies claim is correct. derricks z - scores are for the first test and for the second test. derricks total is, which is less than julies total. c. julies claim is incorrect. they both totaled 150 points on the two exams so neither student did better than the other.

the first stats exam had a mean of 65 and a standard deviation of 10 points; the second had a mean of 75 and a standard deviation of 5 points. derrick scored a 75 on both tests. julie scored a 70 on the first test and an 80 on the second. they both totaled 150 points on the two exams, but julie claims that her total is better. explain. select the correct choice below and, if necessary, fill in the answer boxes within your choice. (round to three decimal places as needed.) a. julies claim is incorrect. derricks z - scores are for the first test and for the second test. derricks total is, which is more than julies total. b. julies claim is correct. derricks z - scores are for the first test and for the second test. derricks total is, which is less than julies total. c. julies claim is incorrect. they both totaled 150 points on the two exams so neither student did better than the other.

Answer

Explanation:

Step1: Recall the z - score formula

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

Step2: Calculate Derrick's z - scores

For the first test: $\mu_1 = 65$, $\sigma_1=10$, $x_1 = 75$. So $z_{1D}=\frac{75 - 65}{10}=\frac{10}{10}=1$. For the second test: $\mu_2 = 75$, $\sigma_2 = 5$, $x_2 = 75$. So $z_{2D}=\frac{75 - 75}{5}=0$. The total z - score for Derrick is $z_D=z_{1D}+z_{2D}=1 + 0=1$.

Step3: Calculate Julie's z - scores

For the first test: $\mu_1 = 65$, $\sigma_1 = 10$, $x_1 = 70$. So $z_{1J}=\frac{70 - 65}{10}=\frac{5}{10}=0.5$. For the second test: $\mu_2 = 75$, $\sigma_2 = 5$, $x_2 = 80$. So $z_{2J}=\frac{80 - 75}{5}=\frac{5}{5}=1$. The total z - score for Julie is $z_J=z_{1J}+z_{2J}=0.5 + 1=1.5$.

Step4: Compare the total z - scores

Since $z_J = 1.5$ and $z_D=1$, Julie's total z - score is higher.

Answer:

B. Julie's claim is correct. Derrick's z - scores are for the first test and for the second test. Derrick's total is 1, which is less than Julie's total of 1.5.