(9).

Use the probability distribution to complete parts (a) and (b) below.

The number of defects per 1000 machine parts inspected

Defects	0	1	2	3	4	5
Probability	0.269	0.300	0.239	0.134	0.045	0.013

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Part 1

(a) Find the mean, variance, and standard deviation of the probability distribution.

The mean is

1.41.4.

(Round to one decimal place as needed.)

Part 2

The variance is

1.51.5.

(Round to one decimal place as needed.)

Part 3

The standard deviation is

1.21.2.

(Round to one decimal place as needed.)

Part 4

(b) Interpret the results.

The mean is

1.41.4,

so the average batch of 1000 machine parts has

The standard deviation is

1.51.5,

so the typical number of defects in a batch of 1000

(Round to one decimal place as needed.)