The general approach to answering this item is to determine first the z-score of the given data and convert the z-scores to percentile. The equation for z-score determination is,
z-score = (X - μ) / σ
where X is the data, μ is the mean or average, and σ is the standard deviation.
(A) at most 2.7 minutes
z-score = (2.7 - 3.2) / 1.6 = -0.3125
This is equivalent to 37.73%
(B) more than 3.5 minutes
z-score = (3.5 - 3.2) / 1.6 = 0.1875
This is equivalent to 57.44%. We are asked for more than so we take,
100 - 57.44% = 42.56%
(C) z-score of 3.2 minutes
z-score = (3.2 - 3.2) / 1.6 = 0
This is equivalent to 50%.
z-score of 3.4 minutes
z-score = (3.4 - 3.2) / 1.6 = 0.125
This is equivalent to 54.97%
The difference of the two percentiles is 4.97%.
