Respuesta :
Answer:
Q3 = 65.7825.
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 = 63.6, \sigma = 2.5[/tex]
Find the value of the quartile Q3. (Hint: Q3 has an area of 0.75 to its left.)
This is the value of X when Z has a pvalue of 0.75. So it is X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 63.6}{2.5}[/tex]
[tex]X - 63.6 = 0.675*2.5[/tex]
[tex]X = 65.7825[/tex]
Q3 = 65.7825.
