Refer to the pictograph of a survey of students at Central Community College. Each symbol represents 10 students in a...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

The chart breaks down a survey of 300 students at Central Community College by age (under or over 30) and education (high school diploma or not). The visual overlap makes clear how many students are in each category and combination. Notably, the group outside both circles (100 students) represents students both under 30 and with a diploma—the largest single group. Observing the chart also reveals that 210 students have diplomas, 90 lack diplomas, 140 are under 30, and 160 are 30 or over. These specific counts make it straightforward to calculate the probability of picking a student with any combination of these attributes.

Step-by-Step Solution

Question 1: Probability of Under 30 OR High School Graduate

Complete Statement:

If one student is selected at random from the 300 surveyed, the chance that the student will be under 30 or a high school graduate or both is ______.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: under 30 or a high school graduate or both
    • Meaning: This looks for any student who is either under 30 years of age, or a high school graduate, or who fits both these criteria.
    • Relation to Chart: Corresponds to all students except those who are age 30+ and do NOT have a high school diploma.
    • Important Implications: In probability, 'or' means the union of categories, so all students in at least one of those groups should be included.
• Statement Breakdown 2:
  • Key Phrase: selected at random from the 300 surveyed
    • Meaning: Every student out of the total 300 has an equal chance of being picked.
    • Relation to Chart: Confirms the denominator in the probability fraction must be 300.
    • Important Implications: The sample space for the probability calculation is 300 students.
• What is needed: The probability that a student chosen at random is under 30, or a high school graduate, or both.

Solution:

• Condensed Solution Implementation: We'll use a complement strategy: subtract the number of students who are neither under 30 nor high school graduates from the total number.
• Necessary Data points: Number of students total: 300. Number of students age 30+ and not high school graduates: 50.
  • Calculations Estimations: 300 total - 50 (age 30+ and not graduates) = 250. So, 250 out of 300 students have at least one of the desired traits. Probability = \(\frac{250}{300} = \frac{5}{6}\).
  • Comparison to Answer Choices: \(\frac{5}{6}\) is the fraction matching the correct choice for this probability.

FINAL ANSWER Blank 1: \(\frac{5}{6}\)

Question 2: Probability of Under 30 AND High School Graduate

Complete Statement:

If one student is selected at random from the 300 surveyed, the chance that the student will be both under 30 and a high school graduate is ______.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: both under 30 and a high school graduate
    • Meaning: This is looking for students who fit both criteria at the same time.
    • Relation to Chart: Represents the overlap section in the Venn diagram of 'Under 30' and 'High School Graduates'.
• Statement Breakdown 2:
  • Key Phrase: selected at random from the 300 surveyed
    • Meaning: Every student is equally likely to be selected.
    • Relation to Chart: The total number of possible outcomes is 300, so the denominator is set.
• What is needed: The probability that a randomly chosen student is both under 30 and a high school graduate.

Solution:

• Condensed Solution Implementation: Look directly at the chart to see the count of students who are both under 30 and have a diploma.
• Necessary Data points: Number of students under 30 and with a diploma: 100. Total students: 300.
  • Calculations Estimations: Probability = \(\frac{100}{300} = \frac{1}{3}\).
  • Comparison to Answer Choices: \(\frac{1}{3}\) matches the answer choice for this probability.

FINAL ANSWER Blank 2: \(\frac{1}{3}\)

Summary

For the first blank, a complement approach (subtracting those who are neither under 30 nor high school graduates) makes the calculation simple. For the second blank, a direct lookup provides the answer. The key steps are careful reading of the wording and accurate identification of the counts in the Venn diagram.

Question Independence Analysis

Both blanks are independent: one asks for a union (OR) and the other for an intersection (AND), so knowing one answer does not give away the other.