Question

10) If the probability of defective bolt
is 0.2 then the mean and SD for the
distribution of defective Bolt in a
*
total of 400 bolt are​

Answer 1

Answer:

6

Step-by-step explanation:

Mean will

np

=n(0.1)

=400(0.1)

=40

And variance will be

np(1−p)

=40(1−0.1)

=40(0.9)

=36

Therefore the standard deviation is

36

=6

Answer 2

Mean = 80 and SD = 8

Given :

The probability of defective bolt is 0.2

To find :

The mean and SD for the distribution of defective Bolt in a total of 400 bolt

Solution :

Step 1 of 3 :

Write down probability

Total number bulb = n = 400

Probability of defective bolt = p = 0.2

Step 2 of 3 :

Find mean

Mean

= np

= 400 × 0.2

= 80

Step 3 of 3 :

Find SD

The required SD

$\displaystyle \sf{ = \sqrt{np(1 - p)} }$

$\displaystyle \sf{ = \sqrt{400 \times 0.2 \times (1 - 0.2)} }$

$\displaystyle \sf{ = \sqrt{400 \times 0.2 \times 0.8} }$

$\displaystyle \sf{ = \sqrt{400 \times \frac{2}{10} \times \frac{8}{10} } }$

$\displaystyle \sf{ = \sqrt{64} }$

$\displaystyle \sf{ = 8}$