Respuesta :
Answer:
x = 209.2
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 z-score 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, or the area to the left of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X, which is the area to the right of X.
Mean of 185 and a standard deviation of 20.
This means that [tex]\mu = 185, \sigma = 20[/tex]
Find the value of x so that the area under the normal curve to the left of x is approximately 0.8869.
This is X when Z has a p-value of 0.8869, so X when Z = 1.21.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.21 = \frac{X - 185}{20}[/tex]
[tex]X - 185 = 20*1.21[/tex]
[tex]X = 209.2[/tex]
So
x = 209.2
