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Answer:
And for this case we know this condition:
By the complement rule we know that:
But since the distribution is symmetrical we know that:
So then the statement for this case is FALSE.
b. False
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
For this case if we define the random variable of interest X and we know that this random variable follows a normal distribution:
And for this case we know this condition:
By the complement rule we know that:
But since the distribution is symmetrical we know that:
So then the statement for this case is FALSE.
b. False