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Answer :
The completion time for the 200-meter backstroke for a female with a z-score of −1.64 is given as follows:
129.5 seconds.
How to obtain the time with the normal distribution?
We must use the z-score formula, as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
- X is the measure.
- [tex]\mu[/tex] is the population mean.
- [tex]\sigma[/tex] is the population standard deviation.
The parameters for this problem are given as follows:
[tex]Z = -1.64, \mu = 141, \sigma = 7[/tex]
Hence the z-score is given as follows:
-1.64 = (X - 141)/7
X - 141 = -1.64 x 7
X = 129.5.
More can be learned about the normal distribution at https://brainly.com/question/25800303
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