In the population of fetuses between the 16th and 25th week of pregnancy the average head diameter is 60.6 (mm) and the corresponding standard deviation 11.2 (mm), the average femur length is 46.8 (mm) with corresponding standard deviation 8.4 (mm). The correlation coefficient of these two quantities is 0.94. (a) What is the best linear prediction for the femur length of a randomly selected fetus from this population given the value of the head diameter? (b) If femur length is normally distributed, compute the probability that the length of the femur of a randomly selected fetus from this population is between 40.5 and 48.9 mm. (c) Assuming that head diameter and femur length follow the bivariate Normal distribution, compute the probability that the length of the femur of a randomly selected fetus from this population is between 40.5 and 48.9 mm given that the diameter of its head was 68.6.
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