Muscle lengths cannot be measured and expressed as an absolute value such as in centimetres. It can be measured functionally by measuring the degree to which a particular muscle allows a movement. Measurement of muscle length along with various other measurements allow researchers to understand musculoskeletal injury in general population.
Using the straight leg raise test, functional length of the hamstring muscle in the general population has approximately a mean of 80 degrees and standard deviation of 13 degrees (degrees of hip flexion). You may assume that hamstring muscle lengths follow a normal distribution.
Use this distribution to answer the following questions. You may use Minitab or Excel for this question but you should include either a hand drawn diagram, or a Minitab distribution curve, with relevant areas shaded in your solution to each part.
a. What is the probability that a randomly selected adult male has a hamstring muscle length between 78 degrees and 83 degrees? Give your answer to 4 dp.
b. The functional muscle length of a randomly selected adult female falls in the lowest 12% of the normal population. What is her muscle length? Give your answer as an integer.
c. A team doctor at a sports club chose 16 athletes from the club and measured their muscle length. What is the probability that the average muscle length of those athletes would have been above 83 degrees? Give your answers to 4 dp.
d. Out of a group of 20 athletes from the sports club, how many would you expect to have a muscle length of 60 degrees or less?