Respuesta :
Using the normal distribution, it is found that 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.
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.
The mean and the standard deviation are given, respectively, by:
[tex]\mu = 20.66, \sigma = 2.4[/tex]
The proportion of students that are 21 or older is one subtracted by the p-value of Z when X = 21, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21 - 20.66}{2.4}[/tex]
Z = 0.14
Z = 0.14 has a p-value of 0.5557.
1 - 0.5557 = 0.4443 = 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.
More can be learned about the normal distribution at https://brainly.com/question/4079902
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