The quartile deviation of a normal distribution with mean 10 and standarddeviation 4 is(a) 0.675.(b) 67.50.(c) 2.70(d) 3.20

The quartile deviation, also known as the semi-interquartile range, is a measure of statistical dispersion. It is half the difference between the upper quartile (Q3) and the lower quartile (Q1).

For a normal distribution, the quartiles can be calculated using the z-scores for the 1st quartile (Q1) and the 3rd quartile (Q3), which are approximately -0.675 and 0.675 respectively.

The formula to convert z-scores to raw scores is X = μ + Zσ, where X is the raw score, μ is the mean, Z is the z-score, and σ is the standard deviation.

So, Q1 = μ + Zσ = 10 + (-0.675)(4) = 7.3 and Q3 = μ + Zσ = 10 + (0.675)(4) = 12.7

The quartile deviation is then (Q3 - Q1) / 2 = (12.7 - 7.3) / 2 = 2.7

So, the correct answer is (c) 2.70.