Question 1194389: A sample of students was selected at random from all
ninth-grade students in a large school district. The
proportion of the students in the sample who were
14 years old was 80%, with an associated margin of
error of 5%. Which of the following is NOT a plausible
number of 14-year-olds in the 3,601 ninth-grade
students in the school district?
A) 2,750
B) 2,900
C) 3,050
D) 3,200
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
It is claimed that 80% of the ninth graders are 14 years old.
We're also told that there's a margin of error of 5%
What this means is that the lowest the percentage can go is 80-5 = 75%
while the highest it can go is 80+5 = 85%
The percentage of 14-year-olds is between 75% and 85%
75% of 3601 = 0.75*3601 = 2700.75 which rounds to 2701
85% of 3601 = 0.85*3601 = 3060.85 which rounds to 3061
The number of 14-year-olds is between 2701 and 3061
This includes the following values
A) 2,750
B) 2,900
C) 3,050
since all three of these values are in the interval mentioned.
Only D) 3,200 is not between 2701 and 3061
Answer: D) 3,200
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