Respuesta :
Answer:
X1 zscore
[tex]Z = -2.09[/tex]
X2 zscore
[tex]Z = -0.89[/tex]
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 = 467, \sigma = 111[/tex]
x1 = 235
Z when [tex]X = 235[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{235 - 467}{111}[/tex]
[tex]Z = -2.09[/tex]
x2 = 368.
Z when [tex]X = 368[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{368 - 467}{111}[/tex]
[tex]Z = -0.89[/tex]
