Respuesta :
Answer:
He needs to score below 68.88 in order to advance to the next round
Step-by-step explanation:
Z-score
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 = 71.5, \sigma = 3.12[/tex]
He needs to score below what value in order to advance to the next round?
Below the 20th percentile, so below the value of X when Z has a pvalue of 0.20. So it is X when [tex]Z = -0.84[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 71.5}{3.12}[/tex]
[tex]X - 71.5 = -0.84*3.12[/tex]
[tex]X = 68.88[/tex]
He needs to score below 68.88 in order to advance to the next round
