Question

A large Distribution of Health Insurance Claims is Right Skewed, with a Mean Of $600 and Standard Deviation of $50. Samples of 36 Claims Each are Selected to form a Sampling Data Base. If a Random Sample of 36 Claims are chosen, what is the probability that the Sample Mean of those claims are less than $20.

Answer 1

To solve this probelm, we need basic results of normal and chi square distribution such as relation between them and asymptotic property of distributions.

1. Sum of square of standard normal variables is chi square

I. E. If there are n standard normal variables then S=sum((xi)^2) will follow chisqure with 'n' degrees of freedom where I goes from 1 to n.

2. In a large distribution ie. When n is large, the distributions tends to standard normal distribution. So we can approximate distributions to standard normal using asymptotic property of them which is used in the 1st and 2nd step in the photo.

The probability can be calculated using software or statistics table. The value that has occurred in the problem is not given in the table of chi-square statistics values, they have to be taken as zero if they go beyond values of extreme numbers in table.