Respuesta :
Answer:
The point is [tex]\mu - 98[/tex], in which [tex]\mu[/tex] is the average per month.
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.
Normal distribution with an average of per month and a standard deviation of $50 per month.
Average of [tex]\mu[/tex], standard deviation [tex]\sigma = 50[/tex]
Find the point in the distribution below which 2.5% of the PCE's fell.
This is below the 2.5th percentile, which is the X when Z has a pvalue of 0.025, so X when Z = -1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - \mu}{50}[/tex]
[tex]X - \mu = -1.96*50[/tex]
[tex]X = \mu - 98[/tex]
The point is [tex]\mu - 98[/tex], in which [tex]\mu[/tex] is the average per month.
