Question

The lengths, in inches, of adult corn snakes have an unknown distribution with mean 56 and standard deviation 10 inches. A sample, with size n=46, is randomly drawn from the population and the sum is taken. What is the probability that the sum is less than 2516 in

Answer 1

Let us denote

Now,

and

and

Since sample size is large enough (>30), we can approximate the sampling distribution of sample means by normal distribution, using Central limit theorem.

We can say that

Now,

The probability that the sum is less than 2516 in