Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let x = the number of the paint cans selected that are defective. Unknown to the man, x follows a hypergeometric distribution. Find the standard deviation of this distribution.
A) 0.739
B) 0.545
C) 1
D) 0.297

Question

Quizplus · Accepted Answer

The standard deviation of a hypergeometric distribution is calculated using the formula: sqrt[n * (k/N) * ((N-k)/N) * ((N-n)/(N-1))], where N is the total number of items, k is the number of defective items, and n is the number of items chosen. Here, N=12, k=3, n=4. Plugging these values into the formula gives approximately 0.739.

Suppose a Man Has Ordered Twelve 1-Gallon Paint Cans of a Particular