Question

The average number of cocktails that residents of my nursing home drink weekly is normally distributed with mean of 12 cocktails with a standard deviation of 3 cocktails. If you take several groups of 12 residents (residential wings) and get the average amount of drinks consumed weekly for these groups, what is the mean and standard deviation of this new distribution?

options:

mean = 144 SD = 36 ,mean = 12 SD = 3 ,mean = 144 SD = 10.39 ,mean = 12 SD = .87

Answer 1

let X be the average number of cocktails that residents of my nursing home drink weekly is normally distributed with mean of 12 cocktails with a standard deviation of 3 cocktails

So, X ~ N(12,9)

, here.

Note that, according to the Central limit theorem if you have a population with finite mean and standard deviation and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

So, since every time we are taking n=12 residents then the average amount of drinks consumed weekly for these groups is given by , and by CLT, we have

So mean is 12, standard deviation of this new distribution is 0.87