MA 117 - Activity Sections 6.1-6.2
Men tend to have longer feet than women. So if you find a really long footprint a the scene of a crime, then in
the absence of any other evidence, you would probably conclude that the criminal was a man. And conversely,
if you find a really short footprint at the scene of a crime, then again in the absence of any other evidence, you
would probably conclude that the criminal was a woman. Where should the cutoff value be for concluding
that the criminal is a man or a woman? What is the probability that you will make a mistake?
Suppose that men’s foot lengths are normally distributed with:
mean µ = 25 cm, and σ = 4 cm.
Women’s foot lengths are normally distributed with:
Mean µ = 19 cm and σ = 3 cm.
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1. Sketch both distributions above, using a scale of 1. LABEL your standard deviation cutoff values clearly.
A reasonable cutoff off point, (the value of cm’s where on one side of the value the foot length is called a
man’s and on the other side of the value it is labeled a woman’s.) would be to take the two means and find a
half way point. SO the median between would be 25 + 19 /2 = 44/2 = 22 cm.
Restate what this 22 means______________________________
a. Using 22 cm as a reference, what is the probability that you will mistakenly identify a man’s foot print as
having come from a woman? That is, what proportion of men’s may be mistaken as women?
b. Using 22 cm as a reference, what is the probability you will mistakenly identify a woman’s footprint as
having come from a man? That is, what proportion of women may be mistaken as men?
c. The police would like to try a different strategy and consider the lowest 8% of the Man’s normal distribution
as the new cutoff for distinguishing between a man’s and a woman’s footprint. What is the new cutoff value in
cm’s? Draw label and shade in the space below to help.
d. Using the new value found above in part C, determine the probability of mistakenly identifying a woman’s
footprint as having come from a man.
e. Comment on how changing the cutoff value affected the probability of error for the two scenarios:
misclassifying a female footprint as a man’s footprint or misclassifying a man’s footprint as a woman’s.
Use all the information gathered above in parts a-e.