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Answer:
And solving for z we have
And we can find the value for z with the following excel code:
"=NORM.INV(0.975,0,1)"
And we got z =1.96
And we can use the complement rule and we got:
And we can find the value for z with the following excel code:
"=NORM.INV(0.8686,0,1)"
And we got z =1.120
And we can find the value for z with the following excel code:
"=NORM.INV(0.67,0,1)"
And we got z =0.440
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
We want this probability:
And solving for z we have
And we can find the value for z with the following excel code:
"=NORM.INV(0.975,0,1)"
And we got z =1.96
For the next part we want to calculate:
And we can use the complement rule and we got:
And we can find the value for z with the following excel code:
"=NORM.INV(0.8686,0,1)"
And we got z =1.120
For the next part we want to calculate:
And we can find the value for z with the following excel code:
"=NORM.INV(0.67,0,1)"
And we got z =0.440