Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$10$ _u-IgNsIkr $7$ j $8$ P $3$ jH-IQ-WKpxOg_PLIKaCnhGTWihcIRHJ|Xyp $6$ pvvsgZDTQhQdp $5$ zsr $9$ i $6$ ekk $6$ zb $5$ bC $7$ FmNdLZp $4$ pOb $9$ hfR... Statistics and Probability Relecting unreasonable cla ms based on average statistics A private college advertised that last year their freshman students, on average, had a score of $1140$ on the SAT. Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements are true, mark the appropriate box. $\newline$ Next year at least one of their freshman students will have a score of at least $1140$ on the SAT. $\newline$ Last year at least one of their freshman students had a score of $1140$ or above on the SAT. $\newline$ Last year some of their freshman students had a score of more than $1380$ on the SAT. $\newline$ Last year, the number of their freshman students who had a score of $1140$ or above on the SAT was equal to the number of their freshman students who had a score of $1140$ or below on the SAT. $\newline$ Last year some of their freshman students had a score of exactly $1140$ on the SAT. $\newline$ None of the above statements are true.

View step-by-step help

Home

Math Problems

Precalculus

Find probabilities using the binomial distribution

Full solution

Q. www-awu.aleks.com/alekscgiVx/lsl.exe/

10

_u-IgNsIkr

7

8

3

jH-IQ-WKpxOg_PLIKaCnhGTWihcIRHJ|Xyp

6

pvvsgZDTQhQdp

5

zsr

9

6

ekk

6

5

7

FmNdLZp

4

pOb

9

hfR... Statistics and Probability Relecting unreasonable cla ms based on average statistics A private college advertised that last year their freshman students, on average, had a score of

1140

on the SAT. Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements are true, mark the appropriate box.

\newline

Next year at least one of their freshman students will have a score of at least

1140

on the SAT.

\newline

Last year at least one of their freshman students had a score of

1140

or above on the SAT.

\newline

Last year some of their freshman students had a score of more than

1380

on the SAT.

\newline

Last year, the number of their freshman students who had a score of

1140

or above on the SAT was equal to the number of their freshman students who had a score of

1140

or below on the SAT.

\newline

Last year some of their freshman students had a score of exactly

1140

on the SAT.

\newline

None of the above statements are true.

Understand Mean Concept: We need to understand what an average (mean) tells us about a set of data. The average score of $1140$ means that when all the SAT scores of the freshman students are added together and then divided by the number of students, the result is $1140$ . This does not provide specific information about individual scores.
Evaluate Future Statement: Let's evaluate the first statement: ＂Next year at least one of their freshman students will have a score of at least $1140$ on the SAT.＂ This statement is about a future event and cannot be guaranteed based on last year's average. Therefore, this statement is not necessarily true.
Consider Last Year's Scores: Now, let's consider the second statement: ＂Last year at least one of their freshman students had a score of $1140$ or above on the SAT.＂ If the average is $1140$ , it is possible that all students scored exactly $1140$ , or some scored below and some above this number to achieve this average. However, without additional information about the distribution of scores, we cannot be certain that there was at least one score of $1140$ or above. Therefore, this statement is not necessarily true.
Analyze Median Property: The third statement is: ＂Last year some of their freshman students had a score of more than $1380$ on the SAT.＂ This statement assumes that there were high outliers that would raise the average to $1140$ . However, without knowing the distribution of the scores, we cannot confirm this. Therefore, this statement is not necessarily true.
Examine Specific Scores: The fourth statement is: ＂Last year, the number of their freshman students who had a score of $1140$ or above on the SAT was equal to the number of their freshman students who had a score of $1140$ or below on the SAT.＂ This statement describes a property of the median, not the mean. The average does not provide this specific information about the distribution of scores. Therefore, this statement is not necessarily true.
Examine Specific Scores: The fourth statement is: ＂Last year, the number of their freshman students who had a score of $1140$ or above on the SAT was equal to the number of their freshman students who had a score of $1140$ or below on the SAT.＂ This statement describes a property of the median, not the mean. The average does not provide this specific information about the distribution of scores. Therefore, this statement is not necessarily true.The fifth statement is: ＂Last year some of their freshman students had a score of exactly $1140$ on the SAT.＂ This could be true if the average is $1140$ , but it is not guaranteed. It is possible that all students scored different values that averaged to $1140$ . Therefore, this statement is not necessarily true.