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Probability Basics 493
views are represented by a value of –50 (the extreme left end of the scale) and the most
conservative possible views are represented by a value of 50 (the extreme right end of
the scale). Suppose a density function is graphed and it is discovered, not surprisingly,
that most people tend to fall near the “middle” and that the curve is bell-shaped and symmetric
to the left and right. What type of distribution does this represent?
5. What is the mathematical probability that a conventional coin, tossed 10 times in a
row, will come up tails on all 10 tosses? Express this as a percentage to five significant
figures. Assume that the probability of heads is 1 in 2, and the probability of tails is also
1 in 2.
6. Imagine a strange coin that can land any of three ways: heads, tails, or “on edge.”
Suppose that the chance of the coin landing on the edge for any given toss is 2 in 20,
the chance of its landing heads is 9 in 20, and the chance of its landing tails is 9 in 20.
If this coin is tossed 10 times in a row, what is the probability of its coming up tails on
all 10 tosses? Express this as a percentage to five significant figures.
7. Imagine a normal distribution that produces the classic bell-shaped curve. Suppose
some aspect of the experiment is varied so that the curve becomes “sharper”; that is, the
peak becomes more pronounced. What happens to the standard deviation? What happens
to the total area under the curve?