Respuesta :
Answer:
Q3 = 65.98 inches.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions 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.
Normally distributed with a mean of 64.9 inches and a standard deviation of 1.6 inches.
This means that [tex]\mu = 64.9, \sigma = 1.6[/tex]
Find Q3, the third quartile that separates the bottom 75% from the top 25%.
This is X when Z has a pvalue of 0.75. So X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 64.9}{1.6}[/tex]
[tex]X - 64.9 = 1.6*0.675[/tex]
[tex]X = 65.98[/tex]
Q3 = 65.98 inches.
