Question

For a normally distributed population with mean u and standard deviation o, the inter-quartile range (IQR) is equal to

(a) μ + 2/3σ
(b) 2/3σ
(c) 4/3σ
(d) μ + σ
(e) 2σ

Answer 1

For a normally distributed population, the IQR correlates to about 2.7 times the standard deviation. The closest estimate from the answer choices is option (c) 4/3σ, which approximates the range covered by the IQR.

Step-by-step explanation:

The question asks for the interquartile range (IQR) of a normally distributed population with a certain mean (μ) and standard deviation (σ). The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

In the context of a normal distribution, this value correlates to approximately 1.35 times the standard deviation on either side of the mean, which adds up to about 2.7σ in total. However, since the given answer choices do not include this value, the closest estimate from the answer choices would be option (c) 4/3σ, as this approximates the range covered by the IQR in a normal distribution.