Respuesta :
Answer:
To be dropped, the client must have debts of $949.40 or lower.
Step-by-step explanation:
When the distribution is normal, we use 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.
In this question:
[tex]\mu = 3027, \sigma = 1060[/tex]
Bottom 2.5%
The 2.5th percentile and lower.
The 2.5th percentile is X when Z has a pvalue of 0.025. So X when Z = -1.96. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - 3027}{1060}[/tex]
[tex]X - 3027 = -1.96*1060[/tex]
[tex]X = 949.4[/tex]
To be dropped, the client must have debts of $949.40 or lower.
Answer:
z-score =-1.96
standard deviation= 193.53
x= 2647.68
Step-by-step explanation:
σx¯=1,06030−−√=193.53
By plugging all the numbers into the formula z=x¯−μσx¯ we find that
−1.96=x¯−3,027193.53
−379.32=x¯−3,027
2,647.68=x¯