Answer to Question #169295 in Statistics and Probability for Piyush

Question

class of 30 of these pupils is used as sample. what is the probability that the class mean is greater than 46 inches

Answer 1

Let $X=$ the class mean: $X\sim N(\mu, \sigma^2/n)$

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

Given $\mu=45, \sigma=2, n=30$

$$P(X>46)=1-P(X\leq 46)$$

$$=1-P(Z\leq\dfrac{46-45}{2/\sqrt{30}})\approx1-P(Z\leq2.7386128)$$

$$\approx1-0.996915\approx0.003085$$