To calculate: The qualifying time for the race with respect to the given condition.
The qualifying time for the race which is the fastest 16% of all applicants is 67 minutes.
Given:
The mean and standard deviation of the running times which are
The athlete has to be in the fastest 16% of all applicants to qualify.
Concept used:
The number of standard deviations away from the mean is known as the Z score.
Z score is calculated using the formula
Calculation:
The Z score for the top 16% is calculated as shown below
With reference to Z table, the required Z score is 0.84 as shown below
The Z score approximately is 1.0
Let X be the qualifying running time and is calculated as shown below
The fastest 16% of the applicants run 67 minutes or above. Thus the qualifying time for the race is 67 minutes.
Chapter 11 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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