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

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

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

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