For each of the following z-score locations in a normal distribution, determine whether the tail is on the left side or the right side of the distribution and find/give the proportion that is located in the tail (There will be two answers for each question and drawn a distrubtion.

a. z = +1.75
b. z = +0.80
c. z = –0.70

a) For this case we have , and this value is higher than 0, so then would be on the right tail. And we can find the probability in the tail like this:

b) For this case we have , and this value is higher than 0, so then would be on the right tail. And we can find the probability in the tail like this:

c) For this case we have , and this value is lower than 0, so then would be on the left tail. And we can find the probability in the tail like this:

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

Part a

For this case we have , and this value is higher than 0, so then would be on the right tail. And we can find the probability in the tail like this:

Part b

For this case we have , and this value is higher than 0, so then would be on the right tail. And we can find the probability in the tail like this:

Part c

For this case we have , and this value is lower than 0, so then would be on the left tail. And we can find the probability in the tail like this:

The results are on the figure attached for this case.

step-by-step explanation:

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step-by-step explanation:

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