Respuesta :
Answer:
80% of the values will occurs above 68.24.
Step-by-step explanation:
Problems of normally distributed samples can be 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 = 80, \sigma = 14[/tex]
Determine the value above which 80 percent of the values will occur.
This is the value of X when Z has a pvalue of 1-0.8 = 0.2.
So this is X when Z = -0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.84 = \frac{X - 80}{14}[/tex]
[tex]X - 80 = -0.84*14[/tex]
[tex]X = 68.24[/tex]
80% of the values will occurs above 68.24.
