Question

Foot Lengths at Crime Scenes: From now on, we will assume that foot lengths are normally distributed. Suppose that men's foot lengths are normally distributed with a mean 25 centimeters and standard deviation 4 centimeters, and women's foot lengths are normally distributed with a mean of 19 centimeters and a standard deviation of 3 centimeters.

1. Determine the probability of mistakenly identifying a woman's footprint as having come from a man using the new cutoff value of 19.36 cm.

Complete all of your calculations by hand, showing all steps of your work, on a piece of paper.

Answer 1

As teh new cutoff for identifying the women's footprint are the one which are less than 19.36 cm

so, we just have to find the probability of man's footprint which are smaller than 19.36 and could be mistakenly identified as woman's footprint.

This is a normal distribution question with

P(x < 19.36)=?
The z-score at x = 19.36 is,


This implies that


PS: you have to refer z score table to find the final probabilities.

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