Normal distribution (3) When you don’t know the standard deviation.

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Presentation transcript:

Normal distribution (3) When you don’t know the standard deviation

The Normal Distribution WRITTEN : … which means the continuous random variable X is normally distributed with mean  and variance  2 (standard deviation  )

Example: A machine produces components whose lengths are normally distributed with a mean of 20cm. Given that 8% of the components produced have a length greater than 20.5cm …. Find the standard deviation P(L>20.5)=8%=0.08

Example A machine produces components whose lengths are normally distributed with a mean of 20cm. Given that 8% of the components produced have a length greater than 20.5cm, find the standard deviation P(L>20.5)=8%=0.08 a P(Z>a)=0.08 P(Z<a)=0.92

Example contd… A machine produces components whose lengths are normally distributed with a mean of 20cm. Given that 8% of the components produced have a length greater than 20.5cm, find the standard deviation P(L>20.5)=8%=0.08 Use inverse normal distribution tables …... a =