Respuesta :
Answer:
0.1069 = 10.69%
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 question:
[tex]\mu = 45, \sigma = 10[/tex]
Between 57 and 69
This is the pvalue of Z when X = 69 subtracted by the pvalue of Z when X = 57. So
X = 69
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{69 - 45}{10}[/tex]
[tex]Z = 2.4[/tex]
[tex]Z = 2.4[/tex] has a pvalue of 0.9918
X = 57
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{57 - 45}{10}[/tex]
[tex]Z = 1.2[/tex]
[tex]Z = 1.2[/tex] has a pvalue of 0.8849
0.9918 - 0.8849 = 0.1069 = 10.69%
