Question

Suppose the people living in a city have a mean score of 50 and a standard deviation of 10 on a measure of concern about the environment. Assume that these concern scores are normally distributed. Using the ​50%, -34%, -​14% ​figures, approximately what percentage of people have a score​ above 30?

Answer 1

It is given that mean scores are normally distributed with mean 50 and standard deviation 10

If x denote the no of people living in city having concern about environment .

Then

Then we need to find the probability that of score above 30 .

where   is the CDF of standard normal distribution .

we can find that easily in R .

Which implies that 97.72 % of the people have score above 30