Answer to Question #202489 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 proportion of students would have marks between 10 and 24? 

Answer 1

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

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

$$P(10<X<24)=P(X<24)-P(X\leq 10)$$

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

$$=P(Z<0.6)-P(Z\leq -0.8)$$

$$\approx0.7881446-0.2742531\approx0.5139$$