Respuesta :
Answer:
GPAs os 2.832 and lower will mean that a track team athlete will be recommended for extra tutoring help
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 = 3.36, \sigma = 1.2[/tex]
Bottom 33%:
The 33rd percentile(X when Z has a pvalue of 0.33) and below.
So we have to find X when Z = -0.44.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.44 = \frac{X - 3.36}{1.2}[/tex]
[tex]X - 3.36 = -0.44*1.2[/tex]
[tex]X = 2.832[/tex]
GPAs os 2.832 and lower will mean that a track team athlete will be recommended for extra tutoring help
