1. The grade point averages of a large population of college students is approximately normally distributed with mean 2.4 and standard deviation 0.8. A. What fraction of the students will possess a grade point average in excess of 3.0? B. What fraction of the students will have GPAs between 2.0 and 3.0?2. If students possessing a grade point average less than 1.9 are dropped from the college, what percentage of the students will be dropped?

(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:

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:

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:

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%.

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step-by-step explanation: