Question

The mean GPA of students in a

neighboring school is 3.1 with a
standard deviation of 0.3. What
percent of students have a GPA
higher than 3.1? *

Answer 1

50% of students have a GPA higher than 3.1.

Explanation:

We are given that the mean GPA of students in a neighboring school is 3.1 with a standard deviation of 0.3.

Assuming that the data follows normal distribution.

Let X = GPA of students in a neighboring school

So, X ~ Normal(
`\mu=3.1,\sigma^(2) =0.3^(2)`)

The z score probability distribution for normal distribution is given by;

Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = population mean GPA = 3.1

`\sigma` = standard deviation = 0.3

Now, the probability that the students have a GPA higher than 3.1 is given by = P(X > 3.1)

P(X > 3.1) = P(
`(X-\mu)/(\sigma)` >
`(3.1-3.1)/(0.3)` ) = P(Z > 0) = 0.50

The above probability is calculated by looking at the value of x = 0 in the z table which has an area of 0.50.

Therefore, 50% of students have a GPA higher than 3.1.