PROBABILITY. 1. PROBABILITY. 4. Probability. Student Na

Running head: PROBABILITY 1
Probability
Student Name
Institution

PROBABILITY 2
Background Information
We are given the following:
The mean foot length for men; μmen= 9.84 inch
The standard deviation of men foot length; μmen= 1.57 inch
The mean foot length for women; μwomen= 7.48 inch
The standard deviation of women foot length; μwomen= 1.18 inch
The cutoff foot length between men and women = 8.66 inch
Question 1
We have to calculate the probability that men’s footprint is less than 8.66 inch; P(x<8.66)
Z = x−μ
σ = 8.66−7.48
1.57 = -0.75159
P(Z< -0.75) = 0.2266
Therefore, the probability that I will mistakenly identify a man’s footprint as having come from a
woman is 0.2266.
Question 2
We have to calculate the probability that women’s footprint is greater than 8.66 inches; P(x>
8.66)
Z = x−μ
σ = 8.66−9.84
1.18 = 1
P(Z>1) = 0.1587
Therefore, the probability that I will mistakenly identify a woman’s footprint as having come
from a man is 0.1587
Question 3
The new error of probability = 0.08