how to convert 90% confidence level into a z score

Question

kropot72 · Answer

You need to use an Inverse Normal Probability Table. My table converts 90% confidence interval to $$z=\pm1.6449$$

anonymous · Answer

but i can use only standard normal table and i have to show how i find the answer step by step

kropot72 · Answer

Just look for the cumulative probability value of 0.45 in your standard normal distribution table. It lies between 0.4495 and 0.4505. The z-scores for these are as follows:
0.4495: z=1.64
0.4505: z=1.65
Now you need to take the average of these two z-scores. The value will not be exactly the same as given by the Inverse Normal Probability Table. Remember to give the positive and negative values.

anonymous · Answer

ok but how did u get 0.45

kropot72 · Answer

The total area under the standardized normal distribution curve corresponds to a cumulative probability of 1. The 90% confidence interval corresponds to an area of 0.9 centered on a mean of 0. 
0.9/2 = 0.45.

anonymous · Answer

thanks

kropot72 · Answer

You're welcome :)