The heights of women at a large university are approximately bell-shaped, with a mean of 64 inches and standard deviation of 2 inches. What is the probability that a randomly selected woman from this university is 66 inches or taller?

What is the probability that three randomly selected women from this university are all 66 inches or shorter? What is the probability that of two randomly selected women, one is 66 inches or shorter and the other is 66 inches or taller?

1 Answer
Andrea B.
Dec 14, 2017

60%; 13,2%

Explanation:

the question wants to know haw many women have an height over 66 inch, that is #bar x+ sigma#
from the graph bottom you can see that they are the (13,6+ 2,1) = 15,7% of the whole number of women of the university.
of course the probability that of one randomly selected women, one is 66 inches or shorter is 100-15,7 =84,,3 %.

The probability that of two randomly selected women, one is 66 inches or shorter and the other is 66 inches or taller is given by the prodoct of the twoo indipendens probalities:
#p= p_1 xx p_2 = 0,843 xx 0,157 xx 100= 13,2%#

finally the probability that three randomly selected women from this university are all 66 inches or shorter is given by #p= p_1^3 =0,843^3 xx 100= 60%#
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