Respuesta :
Answer:
The area under the normal curve from the mean to 118.8. is 0.47
Step-by-step explanation:
When the distribution is normal, we use 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, we have that:
[tex]\mu = 100, \sigma = 10[/tex]
Find the area under the normal curve from the mean to 118.8.
This is the pvalue of Z when X = 118.8 subtracted by the pvalue of Z when X = 100.
X = 118.8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{118.8 - 100}{10}[/tex]
[tex]Z = 1.88[/tex]
[tex]Z = 1.88[/tex] has a pvalue of 0.97
X = 100
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 100}{10}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
0.97 - 0.5 = 0.47
The area under the normal curve from the mean to 118.8. is 0.47
