Answer to Question #155425 in Statistics and Probability for rock 206

Question

suppose the mean weight of all the students in this examination hall is 54 kgs, and the standard deviation is 4 kgs. what percentage of students will fall between 44 to 62 kgs? justify your answer

Answer 1

Let $X$ be the weight of student. If the distribution of $X$ is not normal we cannot say about the percentage of students will fall between 44 to 62 kgs.

If we assume that the weight of student is normally distributed than $X\sim N (\mu, \sigma^2)$.

$$Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1)$$

Given $\mu=54, \sigma=4.$

$$P(44<X<62)=P(X<62)-P(X\leq 44)$$

$$=P(Z<\dfrac{62-54}{4})-P(Z\leq\dfrac{44-54}{4})$$

$$=P(Z<2)-P(Z\leq-2.5)$$

$$\approx0.97725-0.00621=0.97104$$

97.104 % of students will fall between 44 to 62 kgs.