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Using the normal distribution, there is a 0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.
<h3>Normal Probability Distribution</h3>The z-score of a measure X of a normally distributed variable with mean and standard deviation
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
The probability that a randomly selected cyclist will take at least 2.45 hours to complete the race is <u>one subtracted by the p-value of Z when X = 2.45</u>, hence:
Z = -0.1
Z = -0.1 has a p-value of 0.4602.
1 - 0.4602 = 0.5398.
0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.
More can be learned about the normal distribution at brainly.com/question/4079902
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