Please show full work and be specific Quartile 1: 62.2 Median: 63.6 Quartile 3:

Question

Please show full work and be specific

Quartile 1: 62.2

Median: 63.6

Quartile 3: 65.6

Max: 71.1

The graph on the right illustrates the height of a large group of women a. what is the mean height of adult women? b. If one of these women is randomly selected, find the probability that her height is between 56-1 in and 62.2 in. c. If one of these women is randomly selected, find the probability that her height is below 62.2 in. or above 63.6 in. d. If two women are randomly selected, find the probability that they both have heights between 62.2 in. and 63.6 in e. If five women are randomly selected, find the probability that three of them are taller than the mean and the other two are shorter than the mean.

Explanation / Answer

(a)
Mean = (Q1+Q3)/2 = (62.2+65.6)/2 = 63.9

(b)
There is around 25% of population lies between Q1 and minimum value of a box-plot.
Hence probability that a randomly selected woman has height betweeen 56.1 and 62.2 is 0.25.

(c)
There is around 25% of population lies between Q1 and median value of a box-plot.
Hence probability that a randomly selected woman has height betweeen 62.2 and 63.6 is 0.25.

(d)
Required probability = 0.25*0.25 = 0.0625

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