Question

A shipment of 8 similar microcomputers to a retail outlet contains 3 that are defective. If a school makes a random purchase of 2 of these computers, find the probability distribution for the number of defectives? Also, find its mean and standard deviation

Answer 1

Answer on Question #45891 – Math – Statistics and Probability

Problem.

A shipment of 8 similar microcomputers to a retail outlet contains 3 that are defective. If a school makes a random purchase of 2 of these computers, find the probability distribution for the number of defectives? Also, find its mean and standard deviation.

Solution:

There are $8 - 3 = 5$ working microcomputers. There are $\binom{8}{2} = 28$ ways to select 2 computers.

There are $\binom{3}{0}\binom{5}{2} = 10$ ways to select 0 defective computers and 2 working computers.

The probability to select 0 defective computers is

$$P = \frac{10}{28} \approx 0.3571.$$

There are $\binom{3}{1}\binom{5}{1} = 15$ ways to select 1 defective computers and 1 working computers.

The probability to select 1 defective computers is

$$P = \frac{15}{28} \approx 0.5357.$$

There are $\binom{3}{2}\binom{5}{0} = 3$ ways to select 2 defective computers and 0 working computers.

The probability to select 1 defective computers is

$$P = \frac{3}{28} \approx 0.1071.$$$$\text{Mean} = 0 \cdot \frac{10}{28} + 1 \cdot \frac{15}{28} + 2 \cdot \frac{3}{28} = \frac{21}{28} = 0.75.$$ $$\text{Mean of the squares} = 0 \cdot \frac{10}{28} + 1 \cdot \frac{15}{28} + 4 \cdot \frac{3}{28} = \frac{27}{28} \approx 0.9642.$$

Standard deviation = $\sqrt{\text{Mean of the squares} - \text{Mean}^2} = \sqrt{3/14} \approx 0.4629$.

Answer:

Mean = 0.75, Standard deviation = $\sqrt{3/14} \approx 0.4629$.

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