Question

# A local bottling company has determined the number of machine breakdowns per month and their respective...

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:

(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,

1.65

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

So,

0.25

(3)

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

So,

Standard Deviation =

So,

1.1864

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