Respuesta :
Answer:
The normal distribution is explained for the solution of this question.
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 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.
Mean = 25, Standard Deviation = 3.8
This means that [tex]\mu = 25, \sigma = 3.8[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{X - 25}{3.8}[/tex]
If P(X > k) = a
We have to find [tex]X = k[/tex] when Z has a pvalue of 1 - a.
If P(X < k) = a
We have to find [tex]X = k[/tex] when Z has a pvalue of a.
