Interpreting Areas Under Density Curves

  • 1.

    Exam scores from 0 to 100 are uniformly distributed as shown in the density curve below. The area under the curve from 80 to 100 is 0.25. Interpret this area.

    Answers:

    • 25 exams have a score that is neither 80 nor 100

    • 25 exams have a score of 80 or 100

    • 25% of the exam scores are between 80 and 100.

    • 25% of the exam scores are not between 80 and 100.

  • 2.

    Cookies sold each day a store from 0 to 50 cookies are uniformly distributed as shown in the density curve below. The area under the curve from 10 to 20 is 0.5. Interpret this area.

    Answers:

    • 50% of the days cookies were sold, the amount sold was not between 10 and 20.

    • There were 50 days where 10 or 20 cookies were sold.

    • 50% of the days cookies were sold, the amount sold was between 10 and 20.

    • There were 50 days where neither 10 nor 20 cookies were sold.

  • 3.

    Tickets sold for concerts from 0 to 500 tickets are uniformly distributed as shown in the density curve below. The area under the curve from 0 to 100 is 0.2. Interpret this area.

    Answers:

    • 20 concerts sold more than 100 tickets.

    • 20% of the concerts sold more than 100 tickets.

    • 20% of the concerts sold between 0 and 100 tickets.

    • 20 concerts sold between 0 and 100 tickets.

  • 4.

    A critic's movie ratings from 0 to 10 are uniformly distributed as shown in the density curve below. The area under the curve from 6 to 9 is 0.3. Interpret this area.

    Answers:

    • 30% of the ratings are less than or equal to 6 or greater than or equal to 9.

    • 30% of the ratings are from 6 and 9.

    • 30 movies were rated from 6 to 9.

    • 30 movies were rated less than or equal to 6 or greater than or equal to 9.

  • 5.

    The weights of people in a particular country from 0 to 250 pounds are uniformly distributed as shown in the density curve below. The area under the curve from 100 to 150 is 0.33. Interpret this area.

    Answers:

    • 33 people in that country do not weigh between 100 to 150 pounds.

    • 33% of people in that country weigh between 100 to 150 pounds.

    • 33 people in that country weigh between 100 to 150 pounds.

    • 33% of people in that country do not weigh between 100 to 150 pounds.

  • 6.

    Points scored by a team in basketball games from 0 to 100 points are uniformly distributed as shown in the density curve below. The area under the curve from 60 to 80 is 0.5. Interpret this area.

    Answers:

    • 5% of the basketball games the team played, they scored between 60 and 80 points.

    • 50% of the basketball games the team played, they scored between 60 and 80 points.

    • 50 of the basketball games the team played, they scored between 60 and 80 points.

    • 5 of the basketball games the team played, they scored between 60 and 80 points.

  • 7.

    The number of dropouts from a college each year from 0 to 20 dropouts are uniformly distributed as shown in the density curve below. The area under the curve from 8 to 12 is 0.4. Interpret this area.

    Answers:

    • 4% of the years recorded, the college had between 8 and 12 dropouts.

    • For 4 of the years recorded, the college had between 8 and 12 dropouts.

    • For 40 of the years recorded, the college had between 8 and 12 dropouts.

    • 40% of the years recorded, the college had between 8 and 12 dropouts.

  • 8.

    The number of pages in a book read each day from 0 to 75 pages are uniformly distributed as shown in the density curve below. The area under the curve from 0 to 30 is 1.00. Interpret this area.

    Answers:

    • 100% of the days, the number of pages read was between 0 and 30.

    • 1% of the days, the number of pages read was between 0 and 30.

    • 0.1% of the days, the number of pages read was between 0 and 30.

    • 10% of the days, the number of pages read was between 0 and 30.

  • 9.

    The members of a Library each year from 0 to 100 members are uniformly distributed as shown in the density curve below. The area under the curve from 20 to 50 is 0.75. Interpret this area.

    Answers:

    • 25% of the years recorded, the Library had between 20 and 50 members.

    • 75% of the years recorded, the Library had between 20 and 50 members.

    • 75% of the years recorded, the Library did not have between 20 and 50 members.

    • 25% of the years recorded, the Library did not have between 20 and 50 members.

  • 10.

    Pizzas sold each day at a pizzeria from 0 to 100 pizzas are uniformly distributed as shown in the density curve below. The area under the curve from 20 to 80 is 0.6. Interpret this area.

    Answers:

    • 4% of the days, between 20 and 80 pizzas were sold.

    • 60% of the days, between 20 and 80 pizzas were sold.

    • 40% of the days, between 20 and 80 pizzas were sold.

    • 6% of the days, between 20 and 80 pizzas were sold.

  • 11.

    Sick days used by employees at a company from 0 to 10 sick days are uniformly distributed as shown in the density curve below. The area under the curve from 0 to 4 is 0.80. Interpret this area.

    Answers:

    • 80 employees used between 0 and 4 sick days.

    • 8 employees used between 0 and 4 sick days.

    • 80% of the employees used between 0 and 4 sick days.

    • 8% of the employees used between 0 and 4 sick days.

  • 12.

    The length of selected documentaries from 0 to 75 minutes are uniformly distributed as shown in the density curve below. The area under the curve from 30 to 60 is 0.67. Interpret this area.

    Answers:

    • 67 documentaries were between 30 and 60 minutes in length.

    • 67% of the documentaries were not between 30 and 60 minutes in length.

    • 67% of the documentaries were between 30 and 60 minutes in length.

    • 67 documentaries were not between 30 and 60 minutes in length.

  • 13.

    The number of pets owned by families from 0 to 10 pets owned are uniformly distributed as shown in the density curve below. The area under the curve from 1 to 10 is 0.9. Interpret this area.

    Answers:

    • 9 families own between 1 and 10 pets.

    • 90% of the families own between 1 and 10 pets.

    • 9% of the families own between 1 and 10 pets.

    • 90 families own between 1 and 10 pets.

  • 14.

    The number of fish caught a day by fishermen from 0 to 10 fish are uniformly distributed as shown in the density curve below. The area under the curve from 1 to 2 is 0.167. Interpret this area.

    Answers:

    • 167% of the fisherman caught either 1 or 2 fish in a day.

    • 0.167% of the fisherman caught either 1 or 2 fish in a day.

    • 16.7% of the fisherman caught either 1 or 2 fish in a day.

    • 1.67% of the fisherman caught either 1 or 2 fish in a day.

  • 15.

    The number of times students brush their teeth a day from 0 to 5 times are uniformly distributed as shown in the density curve below. The area under the curve from 1 to 2 is 1.00. Interpret this area.

    Answers:

    • 0.1% of the students brush their teeth 1 or 2 times a day.

    • 1% of the students brush their teeth 1 or 2 times a day.

    • 100% of the students brush their teeth 1 or 2 times a day.

    • 10% of the students brush their teeth 1 or 2 times a day.

  • 16.

    The number of chocolate bars sold in a day from 0 to 50 bars are uniformly distributed as shown in the given density curve below. The area under the curve from 20 to 30 is 0.5. Interpret this area.

    Answers:

    • 50% of the days, the number of chocolate bars sold was between 20 and 30.

    • For 5 days, the number of chocolate bars sold was between 20 and 30.

    • 5% of the days, the number of chocolate bars sold was between 20 and 30.

    • For 50 days, the number of chocolate bars sold was between 20 and 30.

  • 17.

    Quiz scores from 0 to 100 are uniformly distributed as shown in the given density curve below. The area under the curve from 60 to 80 is 0.2. Interpret this area.

    Answers:

    • 20 of the quizzes had a score between 60 and 80.

    • 20% of the quiz scores were between 60 and 80.

    • 20% of the quiz scores were not between 60 and 80.

    • 20 of the quizzes did not have a score between 60 and 80.

  • 18.

    Number of engineering majors at a university each year from 0 to 50 students are uniformly distributed as shown in the given density curve below. The area under the curve from 35 to 50 is 0.3. Interpret this area.

    Answers:

    • 30 of the years recorded had between 35 and 50 engineering majors at the university.

    • 30% of the years recorded had between 35 and 50 engineering majors at the university.

    • 3 of the years recorded had between 35 and 50 engineering majors at the university.

    • 3% of the years recorded had between 35 and 50 engineering majors at the university.

  • 19.

    Circus ticket sold for shows from 0 to 500 tickets are uniformly distributed as shown in the given density curve below. The area under the curve from 100 to 200 is 0.25. Interpret this area.

    Answers:

    • 75 circus shows sold between 100 and 200 tickets.

    • 75% of the circus shows sold between 100 and 200 tickets.

    • 25 circus shows sold between 100 and 200 tickets.

    • 25% of the circus shows sold between 100 and 200 tickets.

  • 20.

    The weight of pet dogs from 0 to 250 pounds are uniformly distributed as shown in the given density curve below. The area under the curve from 50 to 100 is 0.33. Interpret this area.

    Answers:

    • 3.3% of the pet dogs did not weigh between 50 and 100 pounds.

    • 3.3% of the pet dogs weighed between 50 and 100 pounds.

    • 33% of the pet dogs did not weigh between 50 and 100 pounds.

    • 33% of the pet dogs weighed between 50 and 100 pounds.

  • 21.

    A critic's TV show ratings from 0 to 10 are uniformly distributed as shown in the given density curve below. The area under the curve from 4 to 7 is 0.6. Interpret this area.

    Answers:

    • 6 TV shows received a rating between 4 and 7.

    • 60% of the TV shows received a rating between 4 and 7.

    • 6% of the TV shows received a rating between 4 and 7.

    • 60 TV shows received a rating between 4 and 7.

  • 22.

    Books read in a year by avid readers from 0 to 25 books are uniformly distributed as shown in the given density curve below. The area under the curve from 5 to 15 is 0.67. Interpret this area.

    Answers:

    • 6.7% of the avid readers read between 5 and 15 books in that year.

    • 67% of the avid readers did not read between 5 and 15 books in that year.

    • 6.7% of the avid readers did not read between 5 and 15 books in that year.

    • 67% of the avid readers read between 5 and 15 books in that year.

  • 23.

    The ages of pet cats in a particular neighborhood from 0 to 10 years old are uniformly distributed as shown in the given density curve below. The area under the curve from 4 to 6 is 0.4. Interpret this area.

    Answers:

    • 40% of the pet cats in the neighborhood were between 4 and 6 years old.

    • 4% of the pet cats in the neighborhood were between 4 and 6 years old.

    • 4 pet cats in the neighborhood were between 4 and 6 years old.

    • 40 pet cats in the neighborhood were between 4 and 6 years old.

  • 24.

    The number of home runs hit by a baseball player in each season from 0 to 25 home runs are uniformly distributed as shown in the given density curve below. The area under the curve from 5 to 20 is 0.75. Interpret this area.

    Answers:

    • For 25% of the seasons, the baseball player hit between 5 and 20 home runs.

    • In 75 seasons, the baseball player hit between 5 and 20 home runs.

    • For 75% of the seasons, the baseball player hit between 5 and 20 home runs.

    • In 25 seasons, the baseball player hit between 5 and 20 home runs.

  • 25.

    The ages of members in an art club from 0 to 100 years old are uniformly distributed as shown in the given density curve below. The area under the curve from 20 to 70 is 0.833. Interpret this area.

    Answers:

    • 8.33% of the members in the art club are between 20 and 70 years old.

    • 8.33% of the members in the art club are not between 20 and 70 years old.

    • 83.3% of the members in the art club are not between 20 and 70 years old.

    • 83.3% of the members in the art club are between 20 and 70 years old.

  • 26.

    Pretzels sold at a store every day from 0 to 100 pretzels are uniformly distributed as shown in the given density curve below. The area under the curve from 20 to 40 is 0.5. Interpret this area.

    Answers:

    • 50% of the days, between 20 and 40 pretzels were sold at the store.

    • For 5 of the days recorded, between 20 and 40 pretzels were sold at the store.

    • For 50 of the days recorded, between 20 and 40 pretzels were sold at the store.

    • 5% of the days, between 20 and 40 pretzels were sold at the store.

  • 27.

    The number of days each employee was late to work at a particular company from 0 to 10 days late are uniformly distributed as shown in the given density curve below. The area under the curve from 1 to 8 is 0.7. Interpret this area.

    Answers:

    • 3% of the employees were late to work between 1 and 8 days.

    • 70% of the employees were late to work between 1 and 8 days.

    • 30% of the employees were late to work between 1 and 8 days.

    • 7% of the employees were late to work between 1 and 8 days.

  • 28.

    The visitors to a zoo each day from 0 to 100 are uniformly distributed as shown in the given density curve below. The area under the curve from 90 to 100 is 0.11. Interpret this area.

    Answers:

    • 11% of the days recorded, there were less than 90 visitors at the zoo.

    • 1.1% of the days recorded, there were between 90 and 100 visitors at the zoo.

    • 1.1% of the days recorded, there were less than 90 visitors at the zoo.

    • 11% of the days recorded, there were between 90 and 100 visitors at the zoo.

  • 29.

    The length of selected horror films from 0 to 75 minutes are uniformly distributed as shown in the given density curve below. The area under the curve from 60 to 75 is 1.00. Interpret this area.

    Answers:

    • 10% of the selected horror films were between 60 and 75 minutes long.

    • 1% of the selected horror films were between 60 and 75 minutes long.

    • 0.1% of the selected horror films were between 60 and 75 minutes long.

    • 100% of the selected horror films were between 60 and 75 minutes long.

  • 30.

    The number of students enrolled in a calculus course at a university each semester from 0 to 50 students are uniformly distributed as shown in the given density curve below. The area under the curve from 10 to 20 is 0.0. Interpret this area.

    Answers:

    • 100% of the semesters had between 10 and 20 students enrolled in a calculus course.

    • 20% of the semesters had between 10 and 20 students enrolled in a calculus course.

    • 0% of the semesters had between 10 and 20 students enrolled in a calculus course.

    • 10% of the semesters had between 10 and 20 students enrolled in a calculus course.

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