Answer to Question #292045 in Statistics and Probability for Joe

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

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