The number of points scored by each team in a tournament is normally distributed, with mean ? = 32 and standard deviation ? = 7. What is the probability of:
a. A team scoring 11 points or fewer?
b. A team scoring more than 15 points?
c. A team scoring between 20 and 40 points?
A. z = 11 - 32 / 7 = -3.0 standard deviations below the mean, which Table A2 shows implies
that the probability of scoring this few points would be .0013
B. z = 15 - 32 / 7 = -2.429 standard deviations below the mean, implying that the probability
of scoring 15 goals or fewer translates into .006. Thus, the probability of scoring more than this
is 1 - .006 = .994
C. Calculating the z-scores of each:
for 20: z = 20 - 32 / 7 = -1.714, thus Pr(X > 20) = 1 - .044 = .956
for 40: z = 40 - 32 / 7 = 1.143, thus Pr(X > 40) = .127
Thus Pr(X > 20) - Pr(X > 40) = .956 - .127 = .829
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