1. ## Simple question

Burger hack claims that the mean number of grams of fat in its Lotta Burger is 24 grams with a standard deviation of 5 grams. If a sample of 50 Lotta Burgers is taken, what is the probability that the sample mean is 25 grams or more?

I think I found the answer but really dont understand why.

ty

2. Originally Posted by Nhimrod
Burger hack claims that the mean number of grams of fat in its Lotta Burger is 24 grams with a standard deviation of 5 grams. If a sample of 50 Lotta Burgers is taken, what is the probability that the sample mean is 25 grams or more?

I think I found the answer but really dont understand why.

ty
The sample size n = 50 is large. The population size N can be assumed infinite.

Then the distribution of $\displaystyle \bar{x}$ is normal with mean $\displaystyle \mu = 24$ and standard deviation $\displaystyle \frac{\sigma}{\sqrt{n}} = \frac{5}{\sqrt{50}} = \frac{1}{\sqrt{2}}$.

Calculate $\displaystyle \Pr(\bar{x} > 25)$.

I get 0.0786 (correct to four decimal places).