Calculating the z Score for 95% Confidence Level - Mathematical Method | Sirsh

[Sirsh]

Hi, I'ld like to know if anyone knows how to find the 'z' score inrelation to a percentage degree of confidence. The question is: Determine the z score that would give a result with a degree of confidence of 95%.

I know that it is, 1.9600. However, I would like to know how to figure this out mathematically.

Thanks,
Sirsh.

 

[gerben]

Hi, I'ld like to know if anyone knows how to find the 'z' score inrelation to a percentage degree of confidence. The question is: Determine the z score that would give a result with a degree of confidence of 95%.

I know that it is, 1.9600. However, I would like to know how to figure this out mathematically.

Thanks,
Sirsh.

It's based on the area under the standard normal distribution:
$$\frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2}z^2}$$

Your question "Determine the z score that would give a result with a degree of confidence of 95%." comes down to "what is the value of z such that the area under the standard normal distribution between -z and z is equal to 0.95?". And it turns out that:

$$\int_{-1.96}^{1.96} \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2}z^2} dz \approx 0.95$$

 

[Sirsh]

Thanks a lot, gerben!