A researcher has found that the mean number of mental illness symptoms for the U.S. population is 10 with a standard deviation of 2 (μ = 10, σ = 2). She takes a sample of 40 persons. What is the...

A researcher has found that the mean number of mental illness symptoms for the U.S. population is 10 with a standard deviation of 2 (μ = 10, σ  = 2).  She takes a sample of 40 persons.

1. What is the probability that the sample mean is greater than 10.6 mental illness symptoms?


2. What is the probability that the sample mean will be between 9.6 and 10.5 symptoms?


3. What is the probability of observing a sample mean less than 10?