# Thread: Standard Deviation with Mean w. binomial problem who will win a race

1. ## Standard Deviation with Mean w. binomial problem who will win a race

mark runs a fouty yard dash in 5.1 w. a standard deviation of .2 seconds
Killio runs it in 5.0 seconds with a standard deviation of .15 seconds. if they race five times what is the probability that mark will win 4 times?

2. Originally Posted by Statisticsperson
mark runs a fouty yard dash in 5.1 w. a standard deviation of .2 seconds
Killio runs it in 5.0 seconds with a standard deviation of .15 seconds. if they race five times what is the probability that mark will win 4 times?
Let X = M - K where M ~ Normal$\displaystyle (\mu_M = 5.1, \sigma_M = 0.2)$ and K ~ Normal$\displaystyle (\mu_K = 5.0, \sigma_K = 0.15)$. Then X follows a normal distribution whose mean and standard deviation can be calculated from here: Normal Difference Distribution -- from Wolfram MathWorld

Calculate p = Pr(X) < 0.

Let Y be the random variable number of times Mark wins. Then Y ~ Binomial(n = 5, p = as calculated above). Calculate Pr(Y = 4).