Question

Question

The heights of seasonal pine saplings have an unknown distribution with mean 273 and standard deviation 15 millimeters.

A sample, with size n = 75, is randomly drawn from the population and the sum of the values is taken. Using the Central

Limit Theorem for Sums, what is the standard deviation for the sample sum distribution?

Answer 1

here's an example i found

Explanation:

The Central Limit Theorem for Sums states that the mean of the normal distribution of sums is equal to the mean of the original distribution times the number of samples, so the mean is (280)(42)=11760. The standard deviation is equal to the original standard deviation multiplied by the square root of the sample size. So, the standard deviation is (12)(42−−√)≈77.769. To find the probability using the Standard Normal Table, we find that the z-scores for the two values, 11815 and 11840, are 0.71 and 1.03 respectively, using the formula z=x−μσ. Using the Standard Normal Table, the area to the left of z=0.71 is 0.7611, and the area to the left of z=1.03 is 0.8485. 0.8485−0.7611=0.0874, so the probability is about 9%.

To find the probability using a calculator, we can put the values into the normalcdf() function as: normalcdf(11815, 11840, 11760, 1242−−√), which gives us a result of 0.0879.