In the article "Age at Menopause in Puebla, Mexico" (Human Biology, Vol. 75, No. 2, pp. 205-206), authors L. Sievert and S. Hautaniemi compared the age of menopause for different populations. Menopause, the last menstrual period, is a universal phenomenon among females. According to the article, the mean age of menopause, surgical or natural, in Puebla, Mexico is 44.8 years with a standard deviation of 5.87 years. Let x denote the mean age of menopause for a sample of females in Puebla, Mexico. (a) For samples of size 40, find the mean and standard deviation of x. Interpret your results in 1 sentence. (5 points) (b) Repeat part (a) with n = 100. (5 points) (c) Using the results from part (a), find the probability that a random sample of 40 women in Puebla have a sample menopause mean greater than 50.0 years old. (10 points)
