Respuesta :
Answer:
The data item is [tex]X = 580[/tex]
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.
Mean of 400 and a standard deviation of 60.
This means that [tex]\mu = 400, \sigma = 60[/tex]
z=3
We have to find X when Z = 3. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]3 = \frac{X - 400}{60}[/tex]
[tex]X - 400 = 3*60[/tex]
[tex]X = 580[/tex]
The data item is [tex]X = 580[/tex]
