Questions: Students A and B took tests on probability in two different sections of prestatistics. Student A scored 90 points on a test with mean 73 points and standard deviation 6 points. Student B scored 91 points on a test with mean 75 points and standard deviation 7 points. Complete parts (a) through (c) below. a. Find the z-score for Student A's test score. What does it mean in this situation? Student A's z-score is 2.83, which means the student's test score is 2.83 standard deviations greater than the mean of the section's scores. (Type an integer or decimal rounded to two decimal places as needed.) b. Find the z-score for Student B's test score. What does it mean in this situation? Student B's z-score is , which means the student's test score is standard deviations greater than (Type an integer or decimal rounded to two decimal places as needed.)

Students A and B took tests on probability in two different sections of prestatistics. Student A scored 90 points on a test with mean 73 points and standard deviation 6 points. Student B scored 91 points on a test with mean 75 points and standard deviation 7 points. Complete parts (a) through (c) below.
a. Find the z-score for Student A's test score. What does it mean in this situation?

Student A's z-score is 2.83, which means the student's test score is 2.83 standard deviations greater than the mean of the section's scores.
(Type an integer or decimal rounded to two decimal places as needed.)
b. Find the z-score for Student B's test score. What does it mean in this situation?

Student B's z-score is , which means the student's test score is standard deviations greater than
(Type an integer or decimal rounded to two decimal places as needed.)

Transcript text: Students A and B took tests on probability in two different sections of prestatistics. Student A scored 90 points on a test with mean 73 points and standard deviation 6 points. Student B scored 91 points on a test with mean 75 points and standard deviation 7 points. Complete parts (a) through (c) below. a. Find the $z$-score for Student A's test score. What does it mean in this situation? Student A's z-score is 2.83 , which means the student's test score is 2.83 standard deviations greater than the mean of the section's scores. (Type an integer or decimal rounded to two decimal places as needed.) b. Find the z -score for Student B's test score. What does it mean in this situation? Student B's z-score is $\square$ , which means the student's test score is $\square$ standard deviations greater than (Type an integer or decimal rounded to two decimal places as needed.)

Solution

Solution Steps

Step 1: Calculate the z-score for Student A

To find the z-score for Student A, we use the formula:

\[ z = \frac{X - \mu}{\sigma} \]

where:

$X = 90$ (Student A's score)
$\mu = 73$ (mean score)
$\sigma = 6$ (standard deviation)

Substituting the values:

\[ z = \frac{90 - 73}{6} = \frac{17}{6} \approx 2.83 \]

Thus, Student A's z-score is $2.83$, which indicates that the student's test score is $2.83$ standard deviations greater than the mean of the section's scores.

Step 2: Calculate the z-score for Student B

Next, we calculate the z-score for Student B using the same formula:

\[ z = \frac{X - \mu}{\sigma} \]

where:

$X = 91$ (Student B's score)
$\mu = 75$ (mean score)
$\sigma = 7$ (standard deviation)

Substituting the values:

\[ z = \frac{91 - 75}{7} = \frac{16}{7} \approx 2.29 \]

Thus, Student B's z-score is $2.29$, which indicates that the student's test score is $2.29$ standard deviations greater than the mean of the section's scores.