 #1
songoku
 2,115
 278
 Homework Statement:

The distance walked by a person each day is assumed to be normally distributed with mean 12 km and standard deviation 0.19 km (for Monday to Friday) and mean 10 km and standard deviation 0.5 km for Saturday
a) In randomly chosen week, find the probability the person walks further on Saturday than on Friday
b) In randomly chosen week, find the probability that the mean distance walked by the person for the 6day period is less than 11 km
 Relevant Equations:

Normal Distribution
Linear Combination of Random Variable
a) Let X = distance walked on Friday and Y = distance walked on Saturday
X ~ N (12, 0.19^{2}) and Y ~ N (10, 0.5^{2})
Let A = Y  X → A ~ N (2 , 0.2861)
P(Y > X) = P(Y  X > 0) = P(A > 0) = 9.2 x 10^{5}
But the answer key is 0.026
Where is my mistake? Thanks
X ~ N (12, 0.19^{2}) and Y ~ N (10, 0.5^{2})
Let A = Y  X → A ~ N (2 , 0.2861)
P(Y > X) = P(Y  X > 0) = P(A > 0) = 9.2 x 10^{5}
But the answer key is 0.026
Where is my mistake? Thanks