Respuesta :
Using the normal distribution, it is found that there is a 0.0985 = 9.85% probability that the mean starting salary offered to these 85 students was $64,750 or more.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, the parameters are given as follows:
[tex]\mu = 64230, \sigma = 3712, n = 85, s = \frac{3712}{\sqrt{85}} = 402.6[/tex]
The probability that the mean starting salary offered to these 85 students was $64,750 or more is one subtracted by the p-value of Z when X = 64750, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64750 - 64230}{402.6}[/tex]
Z = 1.29
Z = 1.29 has a p-value of 0.9015.
1 - 0.9015 = 0.0985.
0.0985 = 9.85% probability that the mean starting salary offered to these 85 students was $64,750 or more.
More can be learned about the normal distribution at https://brainly.com/question/24537145
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