Suppose the population of interest consists of the heights of players on a men’s basketball team in inches which are 76, 78, 79, 80, and 86. How many random samples of size-3 are possible for the population
To determine the number of random samples of size-3 from a population of size 5, we use the combination formula.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of elements in the population and r is the desired sample size. In this case, n = 5 and r = 3.
Plugging in the values, we get:
C(5, 3) = 5! / (3!(5-3)!)
= 5! / (3!2!)
= (5 * 4 * 3!) / (3!2 * 1)
= (5 * 4) / (2 * 1)
= 10 / 2
= 5
Therefore, there are 5 random samples of size-3 possible for the given population.