Assume that the finishing times in a New York City 10-kilometer road race are no

Question

Assume that the finishing times in a New York City 10-kilometer road race are normally distributed with a mean of 51 minutes and a standard deviation of 10 minutes. Let X be a randomly selected finishing time. Find a. P (X > 75) b. P (50 < X < 75) c. P(x < 59) Assume that the finishing times in a New York City 10-kilometer road race are normally distributed with a mean of 51 minutes and a standard deviation of 10 minutes. Let X be a randomly selected finishing time. Find a. P (X > 75) b. P (50 < X < 75) c. P(x < 59) Assume that the finishing times in a New York City 10-kilometer road race are normally distributed with a mean of 51 minutes and a standard deviation of 10 minutes. Let X be a randomly selected finishing time. Find a. P (X > 75) b. P (50 < X < 75) c. P(x < 59)

Explanation / Answer

Mean = 51 minutes

Standard deviation = 10 minutes

P(X < A) = P(Z < (A - mean)/standard deviation)

a) P(X > 75) = 1 - P(X < 75)

= 1 - P(Z < (75 - 51)/10)

= 1 - P(Z < 2.4)

= 1 - 0.9918 (from standard normal distribution table)

= 0.0082

b) P(50 < X < 75) = P(X < 75) - P(X < 50)

= 0.9918 - P(Z < (50-51)/10)

= 0.9918 - P(Z < -0.1)

= 09918 - 0.4602

= 0.5316

c) P(X < 59) = P(Z < (59-51)/10)

= P(Z < 0.8)

= 0.7881

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