aditiniyer wrote:During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week. (Numbered 1 through 7 from monday through Sunday respectively), multiply the result by 3, and adding this to the doubled ages of students in years, rounded to the nearest year. If a class consists of 28 students, what is the probability that the median lucky number in the class will be a non-integer ?
A) 0%
B) 10%
C) 20%
D) 30%
E) 40%
We need to know 2 things to answer this question.
First, each student's lucky number will ALWAYS be an
ODD INTEGER.
We know this because...
lucky number = 7^(student's favorite day of the week - 1,2,3.. or 7) x 3 + (
doubled ages of students in years)
In other words, lucky number = (ODD INTEGER x ODD INTEGER) + EVEN INTEGER
= ODD INTEGER + EVEN INTEGER
= ODD INTEGER
Second, when we have an even number of values (28 values), the MEDIAN equals the average (arithmetic mean) of the two middle-most integers (when all of the integers are arranged in ascending order).
Since all 28 values are guaranteed to be ODD (see point #1 above), then we know that the two middle-most integers will be ODD.
So, the median of the 28 values = (some ODD integer + some ODD integer)/2
= (an even integer)/2
= an integer.
In other words, the median of the 28 values is GUARANTEED to be an integer.
So, P(the median of the lucky numbers will be a non-integer) = 0%
Answer:
A
Cheers,
Brent
