Suppose the distribution of serum cholesterol values in undergraduate men is approximately normally distributed with mean μ = 190 mg/dl and standard deviation σ = 40 mg/dl.
a) What is the probability of selecting someone at random from this population who has a cholesterol value that is less than 180?
b) You take a simple random sample of n = 49 individuals from this population and calculate the mean cholesterol of the sample. Describe the sampling distribution of x-bar?
c) Regarding the mean derived from a sample of n = 49, what is the probability of getting a sample mean that is less than 180? Hint: (Determine P(x-bar ≤ 180).