Question

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 0.263 0.296 0.235 0.150 0.041 0.015
(a) find the mean, variance, and standard deviation of the probability distribution.
the mean is 1.5
(round to one decimal place as needed.)
the variance is 1.5
(round to one decimal place as needed.)
the standard deviation is 1.2
(round to one decimal place as needed.)
(b) interpret the results.
the mean is 1.5, so the average batch of 1000 machine parts has
the standard deviation is 1.2, so the typical number of defects in a batch
of 1000
(round to one decimal place as needed.)
no defects.
at least 2 defects.
1 or 2 defects.

Explanation:

The mean of a probability distribution represents the average value. Here, the mean is \(1.5\), so it means that on average, a batch of \(1000\) machine - parts has \(1.5\) defects. The standard deviation measures the spread or typical deviation from the mean. A standard deviation of \(1.2\) indicates that the number of defects in a batch typically varies around the mean (\(1.5\)) by about \(1.2\).

Answer:

The mean is \(1.5\), so the average batch of \(1000\) machine parts has \(1.5\) defects. The standard deviation is \(1.2\), so the typical number of defects in a batch of \(1000\) varies around the mean by about \(1.2\).