Question

Many teachers are concerned about grade inflation. Assume that GPA is normally distributed with mean μ = 2.6 and standard deviation σ = 0.5. Use this data to answer the following:

a.) What is the probability that a randomly selected student has a GPA of 3.6 or higher? Write answer as decimal rounded to the thousandth place.

b.) What percentage of students has a GPA of 3.0 or lower? Write answer as decimal rounded to the thousandth place.

c.) What proportion of students have GPAs between 2.0 and 2.5? Write answer as decimal rounded to the thousandth place.

d.) Suppose that students with the lowest 5% of GPAs get put on academic probation. Find the cutoff GPA. Write answer as decimal rounded to the hundredth place.

e.) One particular student has a GPA of 4.0. Calculate his z-score. Write answer as decimal rounded to the hundredth place.

Answer 1

a. Here we need to find

As distribution is normal we can convert to z

b.

c.

d. Here we need to find x such that

Using z table we get

So

Hence

e. Here for x=4,