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Statistics and Probability

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Comparing Relative Standing

STATS-4CENFL

Suppose a population is being studied with mean $\mu$ and standard deviation $\sigma$ and consider the following quantities:

i. The value of an observation with a $z$ score of -2.

ii. The value of an observation with a $z$ score of 3.

iii. The value of an observation which is equal to the mean of the population.

iv. The value of an observation which is 2.5 standard deviations smaller than the mean $\mu$.

v. The value of an observation $X_i$ such that $\dfrac{X_i-\mu}{\sigma}=1.5$.

Arranging them from least to greatest would yield:

A

iv, i, iii, v, ii

B

i, iv, iii, ii, v

C

iii, i, iv, v, ii

D

iv, iii, v, i, ii

E

iv, i, iii, ii, v