Question

14 refrigerators of a certain type has been returned to a distributor - 8 of these refrigerators have a defective compressor and 6 have less serious problems. A sample (without replacement) of 4 refrigerators are examined in random order, let X be the number of refrigerators with defective compressor among the examined ones. Answer all questions to 3 decimal places.

1. P(X = 3) =

2. P(1 < X ≤ 3) =

3. What is the expected number of refrigerators with defective compressor among the examined ones?

4. What is the standard deviation of number of refrigerators with defective compressor among the examined ones?

Answer 1

X ̴ HG (N = 14 , M = 8 , n = 4 , x = 3 )

Part 1)

Part 2)

P ( 1 <= X <= 3 ) = 0.916

Part 3)

Mean = nm / N
Mean = 4 * 8 / 14
Mean = 2.286

Part 4)
σ² = m ( N - m ) n ( N - n ) / N² ( N - 1 )
σ² = 8 ( 14 - 8 ) 4 ( 14 - 4 ) / 14² ( 14 - 1 )
σ² = 0.7535

Standard deviation σ = √(0.7535)
Standard deviation σ = √(0.7535)
Standard deviation σ = 0.868