Question

The mean GPA of students in a

Answer 1

Answer:

50% of students have a GPA  higher than 3.1.

Step-by-step 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  = $\frac{X-\mu}{\sigma}$  ~ 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( $\frac{X-\mu}{\sigma}$ > $\frac{3.1-3.1}{0.3}$ ) = 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.