Answer to Question #202490 in Statistics and Probability for Leonie Patrocinio

Question

The Research Methods and Statistic module is almost over. Assume that the total marks were at an average of μ= 18 per assessment, and that the distribution of total marks are normally distributed with σ= 10.

What is the proportion that a student would have a mark more than 24 mark if randomly selected?

Answer 1

Let $X=$ the mark of student: $X\sim N(\mu, \sigma^2)$

Given $\mu=18, \sigma=10.$

$$P(X>24)=1-P(X\leq24)$$

$$=1-P(Z\leq\dfrac{24-18}{10})=1-P(Z\leq 0.6)$$

$$\approx0.247253$$