Challenger (Data file: Challeng) These data from Dalal et al XXXXXXXXXXrecords performance of O-rings for the 23 U.S. space shuttle missions prior to the Challenger disaster of January 20, 1986. For...

Challenger (Data file: Challeng) These data from Dalal et al. (1989) records performance of O-rings for the 23 U.S. space shuttle missions prior to the Challenger disaster of January 20, 1986. For each of the previous missions, the temperature at takeoff and the pressure of a prelaunch test were recorded, along with the number of O-rings that failed out of 6. Use these data to try to understand the probability of failure as a function of temperature, and of temperature and pressure. Use your fitted model to estimate the probability of failure of an O-ring when the temperature was 31°F, the launch temperature on January 20, 1986.