What is the probability of obtaining a sample mean smaller than 1.97 ounces?

Question

 A small bag of Doritos has a mean weight of 2 ounces with a standard deviation of 0.1 ounces. A sample of 30 bags were randomly selected and their weight was measured.  What is the probability of obtaining a sample mean smaller than 1.97 ounces?

Answer 1

Answer: 0.5050

Explanation:

Assume the random variable is called, Xbar. Because we have a distribution of sample means of size 30, we calculate the z-score of 1.97 using Z = (Xbar-mu)/sigma/sqrt(n). In this case, Xbar is 1.97, mu is 2, sigma is 0.1, and n is 30. The term sigma/sqrt(n) is called the standard error.

To calculate the probability of getting a bag smaller than 1.97 ounces, we first find the z-score of 1.97 ounces, so 1.97-2/(0.1/sqrt(30)) = -1.64. Next, we use a Z-table to get P(Z<-1.64) = P(Xbar<1.97) = 0.5050.