### Solution Found!

# Sullivan's Algebra Scores: Frequency to Probabilities Analysis

**Chapter 4, Problem 48**

(choose chapter or problem)

**QUESTION:**

The following data represent the homework scores for the material on Polynomial and Rational Functions in Sullivan’s College Algebra course.

37 |
67 |
76 |
82 |
89 |

48 |
70 |
77 |
83 |
90 |

54 |
72 |
77 |
84 |
90 |

59 |
73 |
77 |
84 |
91 |

61 |
75 |
77 |
84 |
92 |

65 |
75 |
78 |
85 |
95 |

65 |
76 |
80 |
87 |
95 |

67 |
76 |
81 |
88 |
98 |

Source: Michael Sullivan, MyMathlab

(a) Construct a relative frequency distribution with a lower class limit of the first class equal to 30 and a class width of 10.

(b) Draw a relative frequency histogram of the data

(c) Determine the mean and median score.

(d) Describe the shape of the distribution based on the results from parts (b) and (c).

(e) Determine the standard deviation and interquartile range.

(f ) What is the probability a randomly selected student fails the homework (scores less than 70)?

(g) What is the probability a randomly selected student earns an A or B on the homework (scores 80 or higher)?

(h) What is the probability a randomly selected student scores less than 30 on the homework?

### Questions & Answers

**QUESTION:**

The following data represent the homework scores for the material on Polynomial and Rational Functions in Sullivan’s College Algebra course.

37 |
67 |
76 |
82 |
89 |

48 |
70 |
77 |
83 |
90 |

54 |
72 |
77 |
84 |
90 |

59 |
73 |
77 |
84 |
91 |

61 |
75 |
77 |
84 |
92 |

65 |
75 |
78 |
85 |
95 |

65 |
76 |
80 |
87 |
95 |

67 |
76 |
81 |
88 |
98 |

Source: Michael Sullivan, MyMathlab

(a) Construct a relative frequency distribution with a lower class limit of the first class equal to 30 and a class width of 10.

(b) Draw a relative frequency histogram of the data

(c) Determine the mean and median score.

(d) Describe the shape of the distribution based on the results from parts (b) and (c).

(e) Determine the standard deviation and interquartile range.

(f ) What is the probability a randomly selected student fails the homework (scores less than 70)?

(g) What is the probability a randomly selected student earns an A or B on the homework (scores 80 or higher)?

(h) What is the probability a randomly selected student scores less than 30 on the homework?

**ANSWER:**

Step 1 of 7

a) For the given data we construct a relative frequency distribution.

Relative frequency distribution is

\(\text { Relative frequency }=\frac{\text { Frequency of class }}{\text { total frequency }}\)

Class |
Frequency |
Relative Frequency |

30–39 |
1 |
0.025 |

40-49 |
1 |
0.025 |

50-59 |
2 |
0.05 |

60-69 |
5 |
0.125 |

70-79 |
13 |
0.325 |

80-89 |
11 |
0.275 |

90-99 |
7 |
0.175 |

Total |
40 |
1 |

#### Watch The Answer!

##### Sullivan's Algebra Scores: Frequency to Probabilities Analysis

Want To Learn More? To watch the entire video and ALL of the videos in the series:

Explore Sullivan’s College Algebra homework score analysis, from frequency distribution construction to in-depth statistical calculations such as standard deviation. Discover histogram visualizations, mean and median interpretations, and probability estimations for various score thresholds. Utilize Excel functions for precise calculations.