Question: Using the information in A and B, find the probability that the difference in mean BMI for 30 women and 35 men selected independently and at random from the respective populations will exceed 3.20.
Information A.) Janssen et al. [A-10] Studied American ages 60 and over. They estimated the mean body mass index of women over age 60 with normal skeletal muscle to be 23.1 with a standard deviation of 3.7. Using these values as the population mean and standard deviation for women over age 60 with normal skeletal muscle index, find the probability that 45 randomly selected women in this age range with normal skeletal muscle index will have a mean BMI greater than 25.
Information B.) Researchers reported the mean BMI for men ages 60 and older with normal skeletal muscle index to be 24.7 with a standard deviation of 3.3. Using these values as the population mean and standard deviation, find the probability that 50 randomly selected men in this age range with normal skeletal muscle index will have a mean BMI less than 24.