The survey involved 61 students in a classical music lecture class with the following preferences: - 35 students like Wolfgang Amadeus Mozart- 34 students like Ludwig van Beethoven- 30 students like Franz Joseph Haydn- 13 students like both Mozart and Beethoven- 21 students like both Mozart and Haydn- 8 students like all three composersTo analyze these results, a Venn diagram is used. The sets are defined as follows:- M represents students who like Mozart.- B represents students who like Beethoven.- H represents students who like Haydn.**Venn Diagram Explanation:**The Venn diagram shows three intersecting circles, each labeled with M, B, and H, representing the students who like each composer. Each intersection represents various combinations of preferences:- The central intersection of all three circles includes students who like all three composers (8 students).- Intersections between two circles, excluding the central one, represent students who like two composers. - The non-overlapping sections of each circle represent students who like only one composer.**Questions:**(a) How many students like exactly two of these composers?(b) How many students like exactly one of these composers?Students need to use the information provided to fill out the Venn diagram and answer questions (a) and (b) based on the intersecting circles.

Answered: Image /qna-images/answer/59c0f5a4-0ca8-4ef8-954d-d0764e6c20e4.jpg

The 61 students in a classical music lecture class were polled, with the results that 35 like Wolfgang Amadeus Mozart, 34 like Ludwig von Beethoven, 30 like Franz Joseph Haydn, 13 like Mozart and Beethoven, 21 like Mozart and Haydn, 13 like Beethoven and Haydn, and 8 like all three composers. Use a Venn diagram to complete parts (a) through (f) below. Complete the Venn diagram. Let M be the set of students that like Mozart, B be the set of students that like Beethoven, and H be the set of students that like Haydn. M B (a) How many of these students like exactly two of these composers? student(s) (Simplify your answer) (b) How many of these students like exactly one of these composers? student(s)

The 61 students in a classical music lecture class were polled, with the results that 35 like Wolfgang Amadeus Mozart, 34 like Ludwig von Beethoven, 30 like Franz Joseph Haydn, 13 like Mozart and Beethoven, 21 like Mozart and Haydn, 13 like Beethoven and Haydn, and 8 like all three composers. Use a Venn diagram to complete parts (a) through (f) below. Complete the Venn diagram. Let M be the set of students that like Mozart, B be the set of students that like Beethoven, and H be the set of students that like Haydn. M B (a) How many of these students like exactly two of these composers? student(s) (Simplify your answer) (b) How many of these students like exactly one of these composers? student(s)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 13CYU

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