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Complete Question:
Ellen is opening. Cookie shop eat a local middle school . She randomly surveys students to determine The types of cookies they would buy at the cookie shop the results of the surveys are below based on the survey. Which statement is not true?
A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.
B) 22½% of the students surveyed would buy a sugar cookie.
C) If 240 students were to purchase a cookie from the store, approximately 66 students will purchase a peanut butter cookie.
D) Half of the students prefer chocolate chips or oatmeal raisin cookies.
(Table showing the results of her survey is in the attachment below)
Answer:
A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.
Step-by-step Explanation:
STEP 1:
In order to ascertain which of the statements given in the options that is NOT TRUE, let's express the given number of students that would buy the different types of cookies in their PROPORTIONS AND PERCENTAGES in the survey result.
Thus:
Type of Cookie==> no of students => Proportion (no of students of a cookie type ÷ total no of students) => % (each proportion for a cookie type)
Chocolate Chip==> 25 => 0.3125 (25÷80) => 31.25% (0.3125 × 100)
Oatmeal Raisin==> 15 => 0.1875 (15÷850) => 18.75% (0.1875 × 100)
Peanut Butter== 22 => 0.275 (22÷80) => 27.5% (0.275 × 100)
Sugar ==> 18 => 0.225 (18÷80) => 22.5% (0.225 × 100)
STEP 2:
Next step is to consider each statement given in the question to see if they are true or not.
==>OPTION A: If 160 students buy a cookie, approximately 18 students would buy a sugar cookie.
To find out if this is true, multiply the proportion of students who would be buy a sugar cookie (0.255) by 160 = 0.255 × 160 = 36.
If 160 buy a cookie, approximately 36 students would buy a sugar.
Option A IS NOT TRUE.
OPTION B: 22½% of the students surveyed would buy a sugar cookie.
From our calculation in STEP 2, we have:
Sugar ==> 18 => 0.225 (18÷80) => 22.5% (0.225 × 100).
Option B is TRUE. 22.5% of the students would go for sugar cookie.
OPTION C: If 240 students were to purchase a cookie from the store, approximately 66 students will purchase a peanut butter cookie.
Number of students that would buy the peanut butter if 240 students were to get a cookie = proportion of students that opt for peanut butter cookie in the survey (0.275) × 240 = 0.275 × 240 = 66.
Option C is TRUE.
OPTION D: D) Half of the students prefer chocolate chips or oatmeal raisin cookies.
Proportion of students who prefer chocolate chips or oatmeal raisin cookies = 0.3125 + 0.1785 = 0.491
This is approximately 0.5 = ½ of the total number of students.
Option D is TRUE.
Therefore, we can conclude that the statement, "A) If 160 students buy a cookie, approximately 18 students would buy a sugar cookie" is NOT TRUE.
