Given that percent of fat calories that a person consumes in America each day is normally distributed with mean 36 and standard deviation 9.
It is said that one individual is randomly selected .
The central limit theorem states that if you have a population with mean μ and standard deviation σ and with large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed with mean μ and standard deviation σ/√n. where n is sample size.
Here we know population mean μ = 36
population standard deviation = σ = 9
here one individual is selected so sample size n = 1.
So sample mean = 36 and sample standard deviation = σ/√n = 9/√1 = 9.
So X is normally distributed with mean 36 and variance 9^2 = 81. - N(36,81)