Question

A local bottling company has determined the number of machine breakdowns per month and their respective probabilities as shown below.

Number of Breakdowns	Probability
0	.18
1	.32
2	.25
3	.17
4	.08

1. The expected number of machine breakdowns per month is:

2. The probability of at least 3 breakdowns per month is:

3. The standard deviation of machine breakdowns per month is:

Answer 1

(1)

From the given data, the following Table is calculated:

Number of breakdowns (x)	Probability (p)	xp	x2 p
0	0.18	0	0
1	0.32	0.32	0.32
2	0.25	0.50	1.00
3	0.17	0.51	1.53
4	0.08	0.32	1.28
Total =		1.65	4.13

So,

Expected number of machine breakdown per month = E(X) = 1.65

So,

Answer is:

1.65

(2) The probability of at least 3 breakdowns pr month = 0.17 + 0.08 = 0.25

So,

Answer is:

0.25

(3)

Variance= E(X²) - (E(X))² = 4.13 - 1.65² = 1.4075

So,

Standard Deviation =

So,

Answer is:

1.1864