Distribution of the Sample mean: 1. The upper leg length of 20-29 years old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm. a. What is the probability that a randomly selected 20 to 29 years old male has an upper leg length that is less than 40 cm. b. A random sample of 9 males who are 20 to 29 years old is obtained. What is the probability that the mean upper leg length is less than 40 cm? c. What is the probability that a random sample of 12 males who are 20 to 29 years old results in a mean upper leg length that is less than 40 cm? d. What effect does increasing the sample size have on the probability? Provide an explanation for this result. e.A random sample of 15 males who are 20 to 29 years old results in a mean upper leg length of 46 cm. Do you find this result unusual? Why? Distribution of the Sample proportion: 2. Suppose a random sample of n=370 teenagers 13 to 17 years of age was asked if they use social media. Of those surveyed, 264 stated that they do use social media. Find the sample proportion of teenagers 13 to 17 years of age who use social media. 3. According to the Centers for Disease Control and Prevention, 18.8% of school-aged children, aged 6-11 years, were overweight in 2004. In a random sample of 90 school- aged children, aged 6-11 years, what is the probability that at least 19% are overweight