Respuesta :
Answer:
Minimum: $25,200
Maximum: $44,800
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 = 35000, \sigma = 5000[/tex]
What are the minimum and the maximum starting salaries of the middle 95% of the graduates
Minimum: 50 - (95/2) = 2.5th percentile.
Maximum: 50 + (95/2) = 97.5th percentile
2.5th percentile:
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 - 35000}{5000}[/tex]
[tex]X - 35000 = -1.96*5000[/tex]
[tex]X = 25200[/tex]
The minimum is $25,200
97.5th percentile:
X when Z has a pvalue of 0.975. So X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 35000}{5000}[/tex]
[tex]X - 35000 = 1.96*5000[/tex]
[tex]X = 44800[/tex]
The maximum is $44,800
