Question

20% of bolts produced by machine are defective. The mean and standard deviation of defective bolts in total of 900bolts are respectively

Answer 1

• Mean = 180

• Standard Deviation = 12

Given :

• 20% of bolts produced by machine are defective

• Total number of bolts = 900

To find :

• Mean

• Standard Deviation

Solution :

Step 1 of 3 :

Find probability of producing a defective bulb

Here it is given that 20% of bolts produced by machine are defective

Hence probability of producing a defective bulb

= p

$\displaystyle \sf{ = \frac{20}{100} }$

$\displaystyle \sf{ = \frac{1}{5} }$

Step 2 of 3 :

Find the mean

Total number of bolts = n = 900

Mean

= np

$\displaystyle \sf{ = 900 \times \frac{1}{5} }$

$\displaystyle \sf{ = 180}$

Step 3 of 3 :

Find Standard Deviation

Standard Deviation

$\sf = \sqrt{npq}$

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

$\displaystyle \sf{ = \sqrt{900 \times \frac{1}{5} \times \bigg(1 - \frac{1}{5} \bigg) } }$

$\displaystyle \sf{ = \sqrt{900 \times \frac{1}{5} \times \frac{4}{5} } }$

$\displaystyle \sf{ = \sqrt{144 } }$

$\displaystyle \sf{ = 12}$