Respuesta :
Answer:
The swimmer must complete the 200-meter backstroke in no more than 130 seconds.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 141, \sigma = 7[/tex]
Fastest 6%
At most in the 6th percentile, that is, at most a value of X when Z has a pvalue of 0.07. So we have to find X when Z = -1.555.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.555 = \frac{X - 141}{7}[/tex]
[tex]X - 141 = -1.555*7[/tex]
[tex]X = 130[/tex]
The swimmer must complete the 200-meter backstroke in no more than 130 seconds.
The swimmer must complete the 200-meter backstroke in no more than 130 seconds.
Calculation of the time taken should be:
Since 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.
So, here the time taken should be
-1.555= X - 141/7
X - 141 = -1.555 (7)
X = 130
Hence, The swimmer must complete the 200-meter backstroke in no more than 130 seconds.
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