Question

Suppose a 400-kilometer relay is performed by 400 runners where everyone runs a single kilometer. Say that the
mean time for each runner is 5 minutes with a standard deviation of 30 seconds. Use the normal approximation to
calculate the probability that this rally will last at least 33 hours and 45 minutes (You may use the symbol Io in your answer.)

Answer 1

= 5 minutes

= 30 seconds = 0.5 minutes

Sample size, n = 400

Normal approximation: P( < A) = P(Z < (A - )/)

= = 5 minutes

= = = 0.025 minutes

P(the rally will last at least 33 hours and 45 minutes) = P(mean time of a runner is (33x60 + 45)/400 minutes)

= P( > 5.0625) = 1 - P( < 5.0625)

= 1 - P(Z < (5.0625 - 5)/0.025)

= 1 - P(Z < 2.5)

= 1 - 0.9938

= 0.0062