The article “Forecasting Postflight Hip Fracture Probability Using Probabilistic Modeling” (J. Biomech. Engr. 2019) examines the risk of bone breaks for astronauts returning from space, who typically lose density during missions. One quantity the article’s authors model is the midpoint fracture risk index (mFRI), the ratio of applied load to bone strength at which the chance of a fracture is 50–50. The article suggests a uniform distribution on[0.55, 1.45] to model this unitless index value.

a. Calculate the mean and standard deviation of mFRI using the specified model.
b. Determine the cdf of mFRI.

c. What is the probability that mFRI is less than 1? Between 0.75 and 1.25?
d. What is the probability that mFRI is within one standard deviation of its expected value? Within two standard deviations?