The average time to complete a 10K race for a female runner is 64.61 minutes with a standard deviation of 5.18 minutes. Sarah completes her first 10K race in 58.24 minutes. What is Sarah’s z-score? (Round your answer to 2 decimal places.)
Question
The average time to complete a 10K race for a female runner is 64.61 minutes with a standard deviation of 5.18 minutes. Sarah completes her first 10K race in 58.24 minutes. What is Sarah’s z-score? (Round your answer to 2 decimal places.)
Solution
To calculate Sarah's z-score, we need to use the formula:
Z = (X - μ) / σ
where: X = Sarah's time = 58.24 minutes μ = Mean time = 64.61 minutes σ = Standard deviation = 5.18 minutes
Substituting the values into the formula, we get:
Z = (58.24 - 64.61) / 5.18
Solving this, we get:
Z = -6.37 / 5.18
Z = -1.23
So, Sarah's z-score is -1.23 when rounded to two decimal places. This means Sarah's time was 1.23 standard deviations below the average time.
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