Given a normal random variable X with mean µ = 100 and variance σª = 49 if we randomly observe X=30, is this an unusual observation? (a) This would be an unusual observation because it lies less than 3 standard deviations away from the mean. (b) This would not be an unusual observation because it lies less than 3 standard deviations away from the mean. (c) This would be an unusual observation because it lies more than 3 standard deviations away from the mean. (d) This would not be an unusual observation because it lies more than 3 standard deviations away from the mean.

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. Given a normal random variable X with mean μ = 100 and variance o² = 49 if we
randomly observe X=30, is this an unusual observation?
(a) This would be an unusual observation because it lies less than 3 standard
deviations away from the mean.
(b) This would not be an unusual observation because it lies less than 3 standard
deviations away from the mean.
(c) This would be an unusual observation because it lies more than 3 standard
deviations away from the mean.
(d) This would not be an unusual observation because it lies more than 3 standard
deviations away from the mean.
Transcribed Image Text:. Given a normal random variable X with mean μ = 100 and variance o² = 49 if we randomly observe X=30, is this an unusual observation? (a) This would be an unusual observation because it lies less than 3 standard deviations away from the mean. (b) This would not be an unusual observation because it lies less than 3 standard deviations away from the mean. (c) This would be an unusual observation because it lies more than 3 standard deviations away from the mean. (d) This would not be an unusual observation because it lies more than 3 standard deviations away from the mean.
Expert Solution
Step 1: Given Information:

It is given that 

Mean = 100

Variance = 49

Standard deviation = 7

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