I have trouble with the question below. Any help would be much appreciated.
3. The members of the newest recruiting class of a certain military organization are taking their physical conditioning test, and those who score in the bottom 16% will have to retest. If the scores are normally distributed, and have an arithmetic mean of 72, what is the score at or below which recruits have to retest?
(1) There are 500 recruits in the class.
(2) 10 recruits 82 or higher.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
I have the solution and the explanation for the question above but I am not entirely convinced of the explanation.
The solution indicates that those 1- top-scoring recruits make up the top 2% (I agree) of the class as a whole – and since the scores are normally distributed, the top 2% represents the third standard deviation above the mean (this is the bit I do not agree with). The top 0.3% represents the third standard deviation above the mean. The top 2% mark is somewhere in between the second and third standard deviation above the mean. Is it still acceptable to approximate “upwards” to the third standard deviation? Forgive my ignorance if this an acceptable assumption. Any input would be much appreciated. Thank you in advance.
Regards,
Pranav
3. The members of the newest recruiting class of a certain military organization are taking their physical conditioning test, and those who score in the bottom 16% will have to retest. If the scores are normally distributed, and have an arithmetic mean of 72, what is the score at or below which recruits have to retest?
(1) There are 500 recruits in the class.
(2) 10 recruits 82 or higher.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
I have the solution and the explanation for the question above but I am not entirely convinced of the explanation.
The solution indicates that those 1- top-scoring recruits make up the top 2% (I agree) of the class as a whole – and since the scores are normally distributed, the top 2% represents the third standard deviation above the mean (this is the bit I do not agree with). The top 0.3% represents the third standard deviation above the mean. The top 2% mark is somewhere in between the second and third standard deviation above the mean. Is it still acceptable to approximate “upwards” to the third standard deviation? Forgive my ignorance if this an acceptable assumption. Any input would be much appreciated. Thank you in advance.
Regards,
Pranav
