Question

You randomly sample 8 graduate students from an NYU event. 5 of the 8 exhibit higher IQ’s than the median of the general population. The probability of obtaining this result by chance (if those graduate students do not differ in IQ from the general population) is

Answer 1

The probability that five of the eight students exhibit an higher IQ than the median of the general population is 0.21875

Explanation:

The given parameters are;

The number of students in the sample, n = 8

The number of the students, x, that exhibit higher IQ's than the median = 5

The probability of obtaining the given result by chance is given as follows;

P(x) = n!/((n - x)!x!) × pˣ × qⁿ⁻ˣ

The probability that a student exhibit higher IQ's than the median = 0.5 = p

Similarly, we have, the probability that a student exhibit lower IQ's than the median = 0.5 = q

Substituting the known values, gives;

P(5) = (8!/((8 - 5)!×5!)) × 0.5^(5) × 0.5^(8 - 5) = 0.21875

Therefor, the probability that 5 of the 8 students exhibit an higher IQ than the median of the general population, P(5) = 0.21875.