Complete the probability distribution table. (Report probabilities accurate to 4 decimal places.)Find the mean of this probability distribution. (Appropriate rounding rules apply.)

Question

The Sky Ranch is a supplier of aircraft parts. Included in stock are 6 altimeters that are correctly calibrated and two that are not. Three altimeters are randomly selected without replacement. Let the random variable xxrepresent the number that are not correctly calibrated.

Complete the probability distribution table. (Report probabilities accurate to 4 decimal places.)

X P(x)

0
1
2
3

Find the mean of this probability distribution. (Appropriate rounding rules apply.) 

mean = 

Answer 1

Probability x not correctly calibrated out of 3 selected, where x = 0, 1, 2, 3

We are dealing with a hypergeometric distributed variable x

Since only 2 not correctly calibrated P(x=3) = 0

P(x=0) = C(2,0)C(6,2)/C(8,2) = 15/28

P(x=1) = C(2,1)C(6,1)/C(8,2) = 12/28

P(x=2) = C(2,2),C(6,0)/C(8,2) = 1/28

mean = sum x * P(x) for x = 0 to 3:

0 * 15/28 + 1 * 12/28 + 2 * 1/28 + 3 * 0 = 14/28 = 1/2