Question

PLEASE HELP!!!

The probability distribution for the number of defective lava lamps a factory produces is shown in the table. Find the expected number of defective lava lamps in a week.

X 0 1 2 3 4 5 6
P(X) .01 .05 .15 .21 .22 .30 .06

Answer 1

The expected number of defective lava lamps in a week is 3.72.

Explanation:

To find the expected number of defective, we multiply each outcome by its probabilities.

The probability of each outcome is:

P(X = 0) = 0.01

P(X = 1) = 0.05

P(X = 2) = 0.15

P(X = 3) = 0.21

P(X = 4) = 0.22

P(X = 5) = 0.3

P(X = 6) = 0.06

Expected number:

Multiplying each outcome by its probability:

E(X) = 0*0.01 + 1*0.05 + 2*0.15 + 3*0.21 + 4*0.22 + 5*0.3 + 6*0.06 = 3.72

The expected number of defective lava lamps in a week is 3.72.