Question

What is the z-score of 0.05?

Answer 1

Hint: For solving this type of question, we should know how to read standard normal probabilities table. You have to read this table carefully for your values. You have to see the value you get after solving the question in the table and then you will get the value of z-score.

Complete step-by-step solution:
To find the z-score for 0.05, we have to refer the area under Normal Distribution Table as given below:

z	0.03	0.04	0.05	0.06	0.07
1.2	0.3907	0.3925	0.3944	0.3962	0.3980
1.3	0.4082	0.4099	0.4115	0.4131	0.4147
1.4	0.4236	0.4251	0.4265	0.4279	0.4292
1.5	0.4370	0.4382	0.4394	0.4406	0.4418
1.6	0.4484	0.4495	0.4505	0.4515	0.4525
1.7	0.4582	0.4591	0.4599	0.4608	0.4616
1.8	0.4664	0.4671	0.4678	0.4686	0.4693

The z-scores are given along the first column and first row. The table is populated with probability values of the area under the normal curve. The given value is a significant level. We have to find its corresponding confidence level. To do that, do,
0.5 - 0.05 = 0.45
Now, we find that the z-score for 0.45 is the same as the z-score of 0.05. Now if we look in the Normal Distribution Table, then we don’t get either our value or the exact same value as our value. Then we use the nearest value for solving the question.
So, the nearest value of 0.45 in the table is 0.4495. Now move horizontally to the z-score column. BY doing this, we get the value as 1.6. Then we move vertically up to the z-score column. And thus, we get the value as 0.04.
We have to add these two values for getting the final value. So, we get,
1.6 + 0.04 = 1.64
So, the z-score for 0.05 is 1.64.

Note: If your significant value is any value, then by dividing it we get the values of tails, if the confidence interval is given. And then we find the value in the table and then if the exact value is not matching in the table, then the most nearest value will be used.