Question

uppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5 and a standard deviation of 0.37. Using the empirical rule, what percentage of the students have grade point averages that are no more than 3.24

Answer 1

Answer:

$P(x \le 3.24) = 0.97725$

Step-by-step explanation:

Given

$\bar x = 2.5$

$\sigma = 0.37$

Required

Percentage that is not more than 3.24

The above implies that:

$x = 3.24$

Calculate z score

$z = \frac{x - \bar x}{\sigma}$

$z = \frac{3.24 - 2.5}{0.37}$

$z = \frac{0.74}{0.37}$

$z = 2$

So, the probability is represented s:

$P(x \le 3.24) = P(z \le 2)$

From z probability

$P(z \le 2) = 0.97725$

Hence:

$P(x \le 3.24) = 0.97725$