Question

The graph illustrates the distribution of test scores taken by College Algebra students. The maximum possible score on the test was 120, while the mean score was 79 and the standard deviation was 8.

55,63,71,79,87,95,103

Distribution of Test Scores

What is the approximate percentage of students who scored between 79 and 103 on the test?
%

What is the approximate percentage of students who scored lower than 55 on the test?
%

What is the approximate percentage of students who scored between 71 and 79?
%

What is the approximate percentage of students who scored between 63 and 95 on the test?
%

Answer 1

Answer:

Mean p = 79

$standard\ deviation\ \sigma=8$

(a)

103 - 79 - P(79 | X 103) = ① (0) -

103 79 79 – 79 Ó 00 8

  $=\phi (3)-\phi (0)$

$=1-0.0013499-(1-0.5)$

(b)

$P(X<55)=\phi \left ( \frac{55-\mu}{\sigma} \right )$

  $=\phi \left ( \frac{55-79}{8} \right )$

  $=\phi \left ( -3 \right )$

$=1-0.998$

(c)

$P(71\leq X\leq 79)=\phi \left ( \frac{79-79}{8} \right )-\phi \left ( \frac{71-79}{8} \right )$

  $=\phi \left ( 0 \right )-\phi \left ( -1 \right )$

$=1-0.5-[1-0841]$

  

(d)

$P(63\leq X\leq 95)=\phi \left ( \frac{95-79}{8} \right )-\phi\left ( \frac{63-79}{8} \right )$

  $=\phi (2)-\phi(2)$

$=1-0.0227-[1-0.9772]$