SOLUTION: Let x denote the time it takes to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner

Algebra ->  Probability-and-statistics -> SOLUTION: Let x denote the time it takes to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner       Log On


   

Question 924472: Let x denote the time it takes to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race in less than 217.51 minutes?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
mean = 190 minutes , sd = 21 minutes, z+=+blue%28x+-+190%29%2Fblue%2821%29
Using the z-value to determine the Probability:
p( x < 217.51) = P(z < 27.51/21) = P( z < 1.31)
Using a TI calculator 0r similarly a Casio fx-115 ES plus
P( z < 1.31) = normalcdf( -100, 1.31) = .9049 0r 90.49%