Round all answers to 4 decimal places where possible.

Question

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.4 ppm and standard deviation 1.6 ppm. 36 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.

1. What is the distribution of ?  ~ N(Correct,)
2. What is the distribution of ?  ~ N(Correct,)
3. What is the probability that one randomly selected city's waterway will have less than 10.2 ppm pollutants? 
4. For the 36 cities, find the probability that the average amount of pollutants is less than 10.2 ppm. 
5. For part d), is the assumption that the distribution is normal necessary? 
6. 
   

Answer 1

Hi Tiffany.

For the distribution of X (part a), the answer is given by N(mean, standard deviation). The distribution for X-bar (part b), the answer is given by N(mean, standard deviation/sqrt(n)), where n is the number of subjects being studied. In this scenario, n would be 36 and the mean and standard deviation is given as well.

For part c and d, you can do both of those in the calculator if you have a TI-83/84, using the "normalcdf" feature under 2ND VARS. If not, you can do by hand using the z-score formula and use the answer you get to find the percentage on a z-table.

I hope this helps you understand this particular problem and please respond if you want to go in depth with the calculator steps.

Sincerely,

Shaniqua W.