Respuesta :
Answer:
(a) The percentage of GPA's more than 3.0 is 22.7%.
(b) The percentage of GPA's between 2.0 and 3.0 is 46.5%.
(c) The percentage of the students that will be dropped is 26.4%.
Step-by-step explanation:
Let X = the grade point averages of a large population of college students.
The random variable X is normally distributed with mean, μ = 2.4 and standard deviation, σ = 0.8.
(a)
Compute the probability of a student getting a GPA more than 3.0 as follows:
[tex]P(X>3.0)=P(\frac{X-\mu}{\sigma}>\frac{3.0-2.4}{0.8})\\=P(Z>0.75)\\=1-P(Z<0.75)\\=1-0.7734\\=0.2266[/tex]
The percentage of GPA's more than 3.0 is, 0.2266 × 100 = 22.7%
Thus, the percentage of GPA's more than 3.0 is 22.7%.
(b)
Compute the probability of a student getting a GPA between 2.0 and 3.0 as follows:
[tex]P(2.0<X<3.0)=P(\frac{2.0-2.4}{0.8}<\frac{X-\mu}{\sigma}<\frac{3.0-2.4}{0.8})\\=P(-0.50<Z<0.75)\\=P(Z<0.75)-P(Z<-0.5)\\=0.7734-0.3085\\=0.4649[/tex]
The percentage of GPA's between 2.0 and 3.0 is, 0.4649 × 100 = 46.5%.
Thus, the percentage of GPA's between 2.0 and 3.0 is 46.5%.
(c)
Compute the probability of a students getting a GPA less than 1.9 as follows:
[tex]P(X<1.9)=P(\frac{X-\mu}{\sigma}<\frac{1.9-2.4}{0.8})\\=P(Z<-0.625)\=1-P(Z<0.625)\\=1-0.7357\\=0.2643[/tex]
The percentage of GPA's below 1.9 is, 0.2643 × 100 = 26.4%.
Thus, the percentage of the students that will be dropped is 26.4%.
