Answer:
She would have to be 13.36 inches.
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 = 10, \sigma = 4[/tex]
How long would a 10th grade girl's hair have to be so that it is longer than 80% of all girls?
80th percentile, so the value of X when Z has a pvalue of 0.80. So X when Z = 0.84.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.84 = \frac{X - 10}{4}[/tex]
[tex]X - 10 = 4*0.84[/tex]
[tex]X = 13.36[/tex]
