Given that z is a standard normal random variable, find z for each situation. The area between 0 and z is .4750. Answer The area between 0 and z is .2291. Answer The area to the right of z is .1314. Answer The area to the left of z is .6700.

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

step-by-step explanation:

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step-by-step explanation:

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