Question

The time taken to complete a motorcycle race is normally distributed, with an average time (µ) of 2.5 hours and a standard deviation () of 0.5 hours.
What is the probability that a randomly selected cyclist will take at least 2.45 hours to complete the race?

Answer 1

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.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• 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:

$\mu = 2.5, \sigma = 0.5$

The probability that a randomly selected cyclist will take at least 2.45 hours to complete the race is one subtracted by the p-value of Z when X = 2.45, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2.45 - 2.5}{0.5}$

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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