Quiz #3
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to the correct answer in the answer box below.
If X is a normally distributed random variable, what is the
probability that it will assume a value more than 2 standard deviations
above its mean?
(Choose the best answer from the choices given below. Due to rounding, none
of them is exactly equal to the desired probability.)
- [ A ] 0.023
- [ B ] 0.046
- [ C ] 0.050
- [ D ] 0.95
- [ E ] 0.98
The probability that a normal random variable assumes a value within 2
standard deviations of its mean is about 0.954, and so the probability
that a normal random variable assumes a value two or more standard
deviations away from the mean is about 0.046. Since the density of a normal
distribution is symmetric about its mean, the probability
that a normal random variable assumes a value more than 2 standard
deviations below its mean is about 0.023, and the probability
that a normal random variable assumes a value more than 2 standard
deviations above its mean is about 0.023.
(Alternatively, one could use Table 3 to obtain the desired
probability.)