2. In people without diabetes, mean glucose is normally distributed typically with mean 100 mg/dl and standard deviation 20 mg/dl. A blood sugar level less than 140 mg/dL (7.8 mmol/L) is normal. A reading of more than 200 mg/dL (11.1 mmol/L) after two hours indicates diabetes.

Assume that there is a patient has blood sugar normally distributed with mean 135 mg/dL and standard deviation 25 mg/dL.

(a) If only one measurement is made for this person, what is the probability that this person will be misdiagnosed diabetes?

(b) If four measurements are made and the sample mean is calculated, what is the mean and standard deviation of the sampling distribution of the sample mean?

(c) What is the distribution of the sample mean of four measurements and why?

(d) If four measurements are made for that person and the mean is calculated and used to diagnose the person, what is the probability that the person will be misdiagnosed diabetes?

Please can you explain well. I am trying to learn