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The Practice of Statistics | 5th Edition | ISBN: 9781464108730 | Authors: Daren S. Starnes, Josh Tabor
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Swim team Hanover High School has the best womens swimming team in the region. The

Chapter 6, Problem 61

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QUESTION:

Hanover High School has the best women's swimming team in the region. The 400-meter freestyle relay team is undefeated this year. In the 400-meter freestyle relay, each swimmer swims 100 meters. The times, in seconds, for the four swimmers this season are approximately Normally distributed with means and standard deviations as shown. Assume that the swimmer's individual times are independent. Find the probability that the total team time in the 400-meter freestyle relay for a randomly selected race is less than 220 seconds.

\(\begin{array}{lcc} \hline \text { Swimmer } & \text { Mean } & \text { Std. dev. } \\ \text { Wendy } & 55.2 & 2.8 \\ \text { Jill } & 58.0 & 3.0 \\ \text { Carmen } & 56.3 & 2.6 \\ \text { Latrice } & 54.7 & 2.7 \\ \hline \end{array}\)

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QUESTION:

Hanover High School has the best women's swimming team in the region. The 400-meter freestyle relay team is undefeated this year. In the 400-meter freestyle relay, each swimmer swims 100 meters. The times, in seconds, for the four swimmers this season are approximately Normally distributed with means and standard deviations as shown. Assume that the swimmer's individual times are independent. Find the probability that the total team time in the 400-meter freestyle relay for a randomly selected race is less than 220 seconds.

\(\begin{array}{lcc} \hline \text { Swimmer } & \text { Mean } & \text { Std. dev. } \\ \text { Wendy } & 55.2 & 2.8 \\ \text { Jill } & 58.0 & 3.0 \\ \text { Carmen } & 56.3 & 2.6 \\ \text { Latrice } & 54.7 & 2.7 \\ \hline \end{array}\)

ANSWER:

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The data given is:

\(\begin{array}{lcc} \hline \text { Swimmer } & \text { Mean } & \text { Std. dev. } \\ \text { Wendy } & 55.2 & 2.8 \\ \text { Jill } & 58.0 & 3.0 \\ \text { Carmen } & 56.3 & 2.6 \\ \text { Latrice } & 54.7 & 2.7 \\ \hline \end{array}\)

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