Respuesta :
Answer:
0.6826 = 68.26% probability that you have values in this interval.
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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
X~N(8, 1.5)
This means that [tex]\mu = 8, \sigma = 1.5[/tex]
What is the probability that you have values between (6.5, 9.5)?
This is the p-value of Z when X = 9.5 subtracted by the p-value of Z when X = 6.5. So
X = 9.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.5 - 8}{1.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
X = 6.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6.5 - 8}{1.5}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587
0.8413 - 0.1587 = 0.6826
0.6826 = 68.26% probability that you have values in this interval.
