Question

At a community college it is known that the grade point average (GPA) of all students has a distribution which is both mound shaped and symmetric. The mean of the distribution is 2.50 with a standard deviation of 0.5. It has been decided by the Faculty Senate that all students with GPAs in the top 16% will graduate with honors. What is the minimum GPA that qualifies a student to graduate with honors? (Hint: you will need to use the Empirical Rule to answer this question) Select one:

Answer 1

Answer:

3 GPA is the minimum GPA that qualifies a student to graduate with honors.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 2.50

Standard Deviation, σ = 0.5

We are given that the distribution of GPA score is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find minimum GPA in the top 16% students will graduate with honors.

Thus,

$P(z) = 1 - 0.16 = 0.84$

Calculating the corresponding value of z from the normal distribution table, we have,

z = 0.994458

$\displaystyle\frac{x-\mu}{\sigma} = 0.994458\\\\\frac{x - 2.5}{0.5} = 0.994458\\\\x = (0.994458\times 0.5) + 2.5\\x = 2.997229 \approx 3$

Hence, 3 GPA is the minimum GPA that qualifies a student to graduate with honors.