Question

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 205 minutes? Round your answer to four decimal places. P= #2 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 223 to 235 minutes? Round your answer to four decimal places. P=

Answer 1

1)

Given

= 190 , = 21

We convert this to standard normal as

P(X < x) = P(Z < (x - ) / )

So,

P(X < 205) = P( Z < (205 - 190) / 21)

= P(Z < 0.71)

= 0.7611(From Z table)

b)

P(223 < X < 235) = P(X < 235) - P(X < 223)

= P( Z < (235 - 190) / 21) - P( Z < (223 - 190) / 21)

= P(Z < 2.14) - P(Z < 1.57)

= 0.9838 - 0.9418 (From Z table)

= 0.0420