Question

The mean annual cost of car insurance is Rs 9450 and standard deviation of Rs 250. What is the probability that the average insurance cost of a sample of 25 cars will be between Rs 9400 and Rs 9500?

Answer 1

X~N($\mu,\frac{\sigma^2}{n})$

$given~\mu=9450,\sigma = 250,n=25\\ p(\frac{9400-9450}{\frac{250}{\sqrt{25}}}<z<\frac{9500-9450}{\frac{250}{\sqrt{25}}})\\ p(-1<z<1)\\=0.6827$