Gestational diabetes is diagnosed in a patient if one hour a

Gestational diabetes is diagnosed in a patient if one hour after consuming a sugary drink the patient\'s blood sugar level is OVER 140. However, the blood sugar level of a patient is unknown, and a diagnosis has to be made based on a sample or a sample mean being over 140. The blood level will vary from sample to sample, but it is generally believed that the amount of glucose in a blood sample follows a normal distribution with standard deviation 10. Kate\'s mean blood sugar level is 142 (thus, unknown to her doctor she has gestational diabetes), and each blood sample follows a normal distribution with mean 142 (the mean level) and standard deviation 10. What is the probability that her gestational diabetes will be NOT be diagnosed?

A) The probability she will not be diagnosed based on just one sample is 20%, however if the average of 9 samples were taken the probability of not being diagnosed will increase to 60%.

B) The probability she will not be diagnosed based on just one sample is 42.1%, however if the average of 9 samples were taken the probability of not being diagnosed will reduce to 3.6%.

C) The probability she will not be diagnosed based on just one sample is 57.9%, however if the average of 9 samples were taken the probability of not being diagnosed will increase to 72.6%.

D) The probability she will not be diagnosed based on just one sample is 42.1%, however if the average of 9 samples were taken the probability of not being diagnosed will decrease to 27.4%.

Solution