Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds.What is the completion time for the 200-meter backstroke for a female with a z-score of −1.64? (Round answer to 1 decimal place.) 141.0 129.5 130.8 152.5
Question
Suppose the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds.What is the completion time for the 200-meter backstroke for a female with a z-score of −1.64? (Round answer to 1 decimal place.) 141.0 129.5 130.8 152.5
Solution
The z-score is a measure of how many standard deviations an element is from the mean. In this case, a z-score of -1.64 means the swimmer's time is 1.64 standard deviations below the mean.
To find the actual time, we use the formula:
X = μ + Zσ
where: X = actual score (time in this case) μ = mean Z = z-score σ = standard deviation
Substituting the given values:
X = 141 + (-1.64)(7)
X = 141 - 11.48
X = 129.52
So, the completion time for the 200-meter backstroke for a female with a z-score of -1.64 is approximately 129.5 seconds (rounded to one decimal place).
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