Question

MATH 2208 Lab 8 No quiz for Lab 8. Submit questions by uploading a file to Moodle. Question 1 Annie and Kelly have been running partners for years, running 5 kilometre (km) races. Annie's mean time in a 5km race is 29 minutes with a standard deviation of 5 minutes. Kelly's mean time in a 5 km race is 26 minutes with a standard deviation of 7 minutes. In any race the times are independent of each other. a. Find the expected difference in the time between Annie and Kelly's 5 km races. Show your work, including the formula. Formula: Calculation: Answer (no sentence required): b. Find the standard deviation of the difference. Show your work, including the formula. Formula: Calculation: Answer (no sentence required):

having some troubles getting Random variables

Answer 1

Let say annie race time is x and kelly race time is y

x ~ NORMAL (29 min, 5 mins)

y ~ NORMAL (26 mins, 7 mins)

(a) Here let say z = x - y

so Expected difference in the time between Annie and kelly race time = z

E[z] = E[x- y] = E[x] - E[y] = 29 - 26 = 3 min

(b) Here we have to find standard devation of z

VaR[z] = VaR[x] + VaR[y] = 52 + 72 = 74

SD[z] = sqrt(74) = 8.6023 mins