4. The table below gives the mean () and standard deviation (s) of height in cen

Question

4. The table below gives the mean () and standard deviation (s) of height in centimeters of adult Hobbits in each of four regions Region T s north 90 5 south 90 10 east 110 5 west 110 10 Use this information to answer the following two questions (a) Consider a Hobbit who is 100 cm tall. In which region would this Hobbit be tallest, relative to the distribution of heights of Hobbits that region? That is, in which region would the Hobbit have the largest z-score? (a) north (b) south (c) east (d) west (b) If the shape of the distribution of height in each region is approximately normal (ie., bell-shaped), then we know that approximately 95% of the Hobbits in the region are between 80 cm and 100 cm in height (a) north (b) south (c) east (d) west

Explanation / Answer

a) z score for North = (100-90)/5 = 2

z score for South = (100-90)/10 = 1

z score for east = (100-110)/5 = -2

z score for South = (100-110)/10 = -1

So the largest z score is for North area.

Option A is correct.

b) As per the empirical rule, 95% of data lie between 2 standard deviation from the mean.

Hence,

North is the answer.

Option A is correct.

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